A scientist suspects that the food in an ecosystem may have been contaminated with radioactive nitrogen over a period of months. Which of the following substances could be examined for radioactivity to test the hypothesis

A scientist suspects that the food in an ecosystem may have been contaminated with radioactive nitrogen over a period of months. Which of the following substances could be examined for radioactivity to test the hypothesis

the hair produced by humans living in the ecosystem
All of the following are true about injectable contraceptives except Question 8 options: They are reversible between injections. The injections must be repeated every 3 months. They are less painful than giving birth. Continued users are more likely to experience amenorrhea.

All of the following are true about injectable contraceptives except Question 8 options: They are reversible between injections. The injections must be repeated every 3 months. They are less painful than giving birth. Continued users are more likely to experience amenorrhea.

All of the following are true about injectable contraceptives except … Read More...
ECNS 203 – Principles of Economics Extra Credit Instructions – Fall 2015 As we are winding down our semester, I have decided to integrate some current events into our econ studies. Much is going on in the world oil market that pertains directly to what we have been studying this semester – related to both micro and macroeconomics. Therefore, I have decided to offer an extra credit opportunity for you if you are willing to do some research, summarize your findings in a short paper, and bring it to class on Tuesday, December 1st ready to discuss. To earn the extra credit complete the following: 1. Do some research on current issues (last 12 months) discussing world oil supply, demand and pricing. 2. Write a short (300 word minimum) paper on your findings relative to the micro and macro-economic issues found in your research. I especially want you to focus on the following questions: a. Why has the oil price dropped so much? b. Will it stay down? Why or Why Not? c. Does our discussion on production costs and decisions on running plants relevant to this issue? Why? d. Who are the winners and losers from a micro and macro-economic perspective? 3. Bring that paper to class with you on Tuesday, December 1st to submit it to me and discuss your findings. If you complete all three steps, I will award you with 10 extra credit points to be added to your total points earned for the semester. This will be in addition to the up to 20 extra credit points earned by answering the Clicker Questions correctly. Late submittals will not be accepted and you must be in attendance to receive the points. Papers given little to no effort will not be awarded points. In other words, don’t submit a bunch of non-sense and expect credit. Cite your resources using whatever style you prefer.

ECNS 203 – Principles of Economics Extra Credit Instructions – Fall 2015 As we are winding down our semester, I have decided to integrate some current events into our econ studies. Much is going on in the world oil market that pertains directly to what we have been studying this semester – related to both micro and macroeconomics. Therefore, I have decided to offer an extra credit opportunity for you if you are willing to do some research, summarize your findings in a short paper, and bring it to class on Tuesday, December 1st ready to discuss. To earn the extra credit complete the following: 1. Do some research on current issues (last 12 months) discussing world oil supply, demand and pricing. 2. Write a short (300 word minimum) paper on your findings relative to the micro and macro-economic issues found in your research. I especially want you to focus on the following questions: a. Why has the oil price dropped so much? b. Will it stay down? Why or Why Not? c. Does our discussion on production costs and decisions on running plants relevant to this issue? Why? d. Who are the winners and losers from a micro and macro-economic perspective? 3. Bring that paper to class with you on Tuesday, December 1st to submit it to me and discuss your findings. If you complete all three steps, I will award you with 10 extra credit points to be added to your total points earned for the semester. This will be in addition to the up to 20 extra credit points earned by answering the Clicker Questions correctly. Late submittals will not be accepted and you must be in attendance to receive the points. Papers given little to no effort will not be awarded points. In other words, don’t submit a bunch of non-sense and expect credit. Cite your resources using whatever style you prefer.

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Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n<D≪N. What is the sample space? If we are interested in knowing the number (count) of defective parts in the sample space, describe how, the concept of a random variable could help. Define a random variable Y and describe what values the random variable Y can take? What does it mean if we say Y=5? Q17. Suppose an experiment consists of tossing two fair coins. Let Y denote the number of heads appearing. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=1? What are the probabilities associated with each outcome? What is the sum of the probabilities associated with all possible values that Y can take? Q18. A lot, consisting of 100 fuses, is inspected by the following procedure. Five fuses are chosen at random and tested: if all 5 fuses pass the inspection, the lot is accepted. Suppose that the lot contains 20 defective fuses. What is the probability of accepting the lot? Define the random variable, its purpose, and the formula/concept that you would use. Q19. In a small pond there are 50 fish, 10 of which have been tagged. If a fisherman’s catch consists of 7 fish, selected at random and without replacement. Give an example of a random variable that can be defined if we are interested in knowing the number of tagged fish that are caught? What is the probability that exactly 2 tagged fish are caught? Define the random variable, its purpose, and the formula/concept that you would use. Applied to Quality Control Q20. My manufacturing firm makes 100 cars every day out of which 10 are defective; the quality control inspector tests drives 5 different cars. Based on the sample, the quality control inspector will make a generalization about the whole batch of 100 cars that I have on that day. Let d denote the number of defective cars in the sample What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective- call this P(d=0); (b) 20% of the cars are defective- call this P(d=1); (c) 40% of the cars are defective- call this P(d=2); (d) 60% of the cars are defective- call this P(d=3),(e) 80% of the cars are defective- call this P(d=4), and (f) 100% of the cars are defective- call this P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Q21. Assume that the quality control inspector is selecting 1 car at a time and the car that he tested is put back in the pool of possible cars that he can test (sample with replacement). Let d denote the number of defective cars in the sample (n) What are the values that d can take (given the information provided above)? What is the probability that the quality control inspector will conclude that: (a) 0% of the cars are defective, (b) 20% of the cars are defective, (c) 40% of the cars are defective, (d) 60% of the cars are defective, (e) 80% of the cars are defective, and (f) 100% of the cars are defective. Let’s call these P(d=0)….P(d=5) What is P(d=0)+ P(d=1)+ P(d=2)+ P(d=3)+ P(d=4)+ P(d=5) Let’s assume that the quality control inspector has been doing the testing for a while (say for the past 1000 days). What is the average # of defective cars that he found? Interesting Problems Q22. A closet contains n pairs of shoes. If 2r shoes are chosen at random (2r<n), what is the probability that there will be no matching pair in the sample? Q23. In a draft lottery containing the 366 days of the leap year, what is the probability that the first 180 days drawn (without replacement) are evenly distributed among the 12 months? What is the probability that the first 30 days drawn contain none from September? Q25. You and I play a coin-tossing game. If the coin falls heads I score one, if tails, you score one. In the beginning, the score is zero. What is the probability that after 2n throws our scores are equal? What is the probability that after 2n+1 throws my score is three more than yours?

Assignment 2 Conditional Probability, Bayes Theorem, and Random Variables Conditional Probability and Bayes’ Theorem Problems 1-14 from Problem Set on Conditional Probability and Bayes’ Theorem I am including all the question here so that there is no confusion. Q1. Pair of six sided dices are rolled and the outcome is noted: What is the sample space? What is the size of the sample space? Suppose all we are interested in is the sum of the two outcomes. What is the probability that the sum of the two is 6? 7? 8? (Note: This can be solved using both enumeration and conditional probability method). Here, it makes more sense to use the enumeration approach than conditional probability. It is, however, listed here to set the stage for Q5. What is the probability that the sum of the two is above 5 and the two numbers are equal? Express this question in terms of events A, B, and set operators. What is the probability that the sum of the two is above 5 or the two numbers are equal? Express this question in terms of events A, B, and set operators. Q2. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.3 What is the value of (a) P(A|B) and (b) P(B|A) Q3. At a fair, a vendor has 25 helium balloons on strings: 10 balloons are yellow, 8 are red, and 7 are green. A balloon is selected at random and sold. Given that the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow? Q4. A bowl contains seven blue chips and three red chips. Two chips are to be drawn at random and without replacement. What is the probability that the fist chip is a red chip and the second a blue? Express this question in terms of events A, B, and set operators and use conditional probability. Q5. Three six sided dices are rolled and the outcome is noted: What is the size of the sample space? What is the probability that the sum of the three numbers is 6? 13? 18? Solve using conditional probability How does the concept of conditional probability help? Q6. A grade school boy has 5 blue and four white marbles in his left pocket and four blue and five white marbles in his right pocket. If he transfers one marble at random from his left pocket to his right pocket, what is the probability of his then drawing a blue marble from his right pocket? Q7. In a certain factory, machine I, II, and III are all producing springs of the same length. Of their production, machines I, II, and III produce 2%, 1%, and 3% defective springs respectively. Of the total production of springs in the factory, machine I produces 35%, machine II produces 25%, and machine III produces 40%. If one spring is selected at random from the total springs produced in a day, what is the probability that it is defective? Given that the selected spring is defective, what is the probability that it was produced on machine III? Q8. Bowl B1 contains 2 white chips, bowl B2 contains 2 red chips, bowl B3 contains 2 white and 2 red chips, and Bowl B4 contains 3 white chips and 1 red chip. The probabilities of selecting bowl B1, B2, B3, and B4 are 1/2, 1/4, 1/8, and 1/8 respectively. A bowl is selected using these probabilities, and a chip is then drawn at random. Find P(W), the probability of drawing a white chip P(B1|W): the probability that bowl B1 was selected, given that a white chip was drawn. Q9. A pap smear is a screening procedure used to detect cervical cancer. For women with this cancer, there are about 16% false negative. For women without cervical cancer, there are about 19% false positive. In the US, there are about 8 women in 100,000 who have this cancer. What is the probability that a woman who has been tested positive actually has cervical cancer? Q10. There is a new diagnostic test for a disease that occurs in about 0.05% of the population. The test is not perfect but will detect a person with the disease 99% of the time. It will, however, say that a person without the disease has the disease about 3% of the time. A person is selected at random from the population and the test indicates that this person has the disease. What are the conditional probabilities that The person has the disease The person does not have the disease Q11. Consider two urns: the first contains two white and seven black balls, and the second contains five white and six black balls. We flip a fair coin and then draw a ball from the first urn or the second urn depending on whether the outcome was a head or a tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? Q12. In answering a question on a multiple-choice test a student either knows the answer or guesses. Let p be the probability that she knows the answer. Assume that a student who guesses at the answer will be correct with probability 1/m where m is the number of multiple choice alternatives. What is the conditional probability that a student knew the answer given that she answered it correctly? Q13. A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy persons tested (i.e., if a healthy person is tested, then, with probability 0.01, the test result will imply that he has the disease.). If 0.5% of the population actually have the disease, what is the probability a person has the disease given that his test results are positive? Q14. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn, c additional balls of the same color are put in it with it. Now suppose that we draw another ball. What is the probability that the first ball drawn was black given that the second ball drawn was red? Random Variables Q15. Suppose an experiment consists of tossing two six sided fair dice and observing the outcomes. What is the sample space? Let Y denote the sum of the two numbers that appear on the dice. Define Y to be a random variable. What are the values that the random variable Y can take? What does it mean if we say Y=7? What does it mean if I say that Y<7? Q16. Suppose an experiment consists of picking a sample of size n from a population of size N. Assume that n≪N. Also, assume that the population contains D defective parts and N-D non defective parts, where n

It takes about 30 doubling times for a cancer cell to form a tumor that is large enough to be felt through the skin with hands. Calculate how many months it would take for the cells to form a tumor that could be felt if the doubling rate is two months.

It takes about 30 doubling times for a cancer cell to form a tumor that is large enough to be felt through the skin with hands. Calculate how many months it would take for the cells to form a tumor that could be felt if the doubling rate is two months.

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The uterus remains in the pelvic cavity for the first 3 months, after which the fundus expands and pushes the uterus into the Question 39 options: thoracic cavity cervix abdominal cavity spine

The uterus remains in the pelvic cavity for the first 3 months, after which the fundus expands and pushes the uterus into the Question 39 options: thoracic cavity cervix abdominal cavity spine

The uterus remains in the pelvic cavity for the first … Read More...
Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11<Z<0.22) (f) P(-0.11<Z<0.5) Q.19. Use normal distribution table to find the missing values (?). (a) P(Z< ?)=0.40 (b) P(Z< ?)=0.76 (c) P(Z> ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11 ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

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In case the body have to stay in lower temperature for extended time period (more than 1 hour), how does the body regulate its response?

In case the body have to stay in lower temperature for extended time period (more than 1 hour), how does the body regulate its response?

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STUDENT GRADER Total Score I am submitting my own work, and I understand penalties will be assessed if I submit work for credit that is not my own. Print Name ID Number Sign Name Date # Points Score 1 4 2 8 3 6 4 12 5 4 6 10 7 8 8 6 9 6 Weeks late Adjusted Score Estimated Work Hours 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Overall Weight Adjusted Score: Deduct 20% from score for each week late Problem 1. Sketch circuits for the following logic equations. Y <= (A and B and C) or not ((A and not B and C and not D) or not (B or D)); X <= (A xor (B and C) xor not D) or (not (B xor C) and not (C or D)) Problem 2. Sketch circuits and write VHDL assignment statements for the following equations. F = m(1, 2, 6) F = M(0, 7) Problem 3. Write logic assignment statements for the following circuit. Problem 4: Sketch circuits and write VHDL assignment statements for the truth tables below. Problem 5: Sketch POS circuits for the 2XOR and 2XNOR functions. Problem 6: Sketch the circuit described by the netlist shown, and complete the timing diagram for the stimulus shown to document the circuit’s response to the example stimulus. Use a 100ns vertical grid in your timing diagram, and show all inputs and outputs. Problem 7: Create a truth table that corresponds to the simulation shown below. Show all input and output values in the truth table, and sketch a logic circuit that could have been used to create the waveform. Problem 8. The Seattle Mariners haven’t had a stolen base in 6 months, and the manager decided it was because the other teams were reading his signals to the base runners. He came up with a new set of signals (pulling on his EAR, lifting one LEG, patting the top of his HEAD, and BOWing) to indicate when runners should attempt to steal a base. A runner should STEAL a base if and only if the manager pulls his EAR and BOWs while patting his HEAD, or if he lifts his LEG and pats his HEAD without BOWing, or anytime he pulls his EAR without lifting his LEG. Sketch a minimal circuit that could be used to indicate when a runner should steal a base. Problem 9. A room has four doors and four light switches (one by each door). Sketch a circuit that allows the four switches to control the light – each switch should be able to turn the light on if it is currently off, and off if it is currently on. Note that it will not be possible to associate a given switch position with “light on” or “light off” – simply moving any switch should modify the light’s status.

STUDENT GRADER Total Score I am submitting my own work, and I understand penalties will be assessed if I submit work for credit that is not my own. Print Name ID Number Sign Name Date # Points Score 1 4 2 8 3 6 4 12 5 4 6 10 7 8 8 6 9 6 Weeks late Adjusted Score Estimated Work Hours 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Overall Weight Adjusted Score: Deduct 20% from score for each week late Problem 1. Sketch circuits for the following logic equations. Y <= (A and B and C) or not ((A and not B and C and not D) or not (B or D)); X <= (A xor (B and C) xor not D) or (not (B xor C) and not (C or D)) Problem 2. Sketch circuits and write VHDL assignment statements for the following equations. F = m(1, 2, 6) F = M(0, 7) Problem 3. Write logic assignment statements for the following circuit. Problem 4: Sketch circuits and write VHDL assignment statements for the truth tables below. Problem 5: Sketch POS circuits for the 2XOR and 2XNOR functions. Problem 6: Sketch the circuit described by the netlist shown, and complete the timing diagram for the stimulus shown to document the circuit’s response to the example stimulus. Use a 100ns vertical grid in your timing diagram, and show all inputs and outputs. Problem 7: Create a truth table that corresponds to the simulation shown below. Show all input and output values in the truth table, and sketch a logic circuit that could have been used to create the waveform. Problem 8. The Seattle Mariners haven’t had a stolen base in 6 months, and the manager decided it was because the other teams were reading his signals to the base runners. He came up with a new set of signals (pulling on his EAR, lifting one LEG, patting the top of his HEAD, and BOWing) to indicate when runners should attempt to steal a base. A runner should STEAL a base if and only if the manager pulls his EAR and BOWs while patting his HEAD, or if he lifts his LEG and pats his HEAD without BOWing, or anytime he pulls his EAR without lifting his LEG. Sketch a minimal circuit that could be used to indicate when a runner should steal a base. Problem 9. A room has four doors and four light switches (one by each door). Sketch a circuit that allows the four switches to control the light – each switch should be able to turn the light on if it is currently off, and off if it is currently on. Note that it will not be possible to associate a given switch position with “light on” or “light off” – simply moving any switch should modify the light’s status.

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