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Lab on Confidence Intervals The story: Studies have shown that the random variable X, the processing time required to do a multiplication on a new 3-D computer, is normally distributed with mean and standard deviation 2 microseconds. A random sample of 16 observations is to be taken (i.e. 16 random multiplications will be performed and the time that it takes to perform each one of them will be annotated). The sample mean will be calculated. Part 1- The very basics 1. Before we collect the random sample, what can we say about the sampling distribution of ? 2. Before we collect the random sample, what is the probability that the sample mean will have a value that is greater than or equal to , and less than or equal to In other words, what is the probability that the sample mean is within 0.98 microseconds ( ) of the true (unknown) mean time? 3. A random sample was taken (i.e.16 multiplications were done) and the processing times were as follows: 42.65 45.15 39.32 44.44 41.63 41.54 41.59 45.68 46.50 41.35 44.37 40.27 43.87 43.79 43.28 40.70 Round the times to the nearest tenth (e.g. 42.65 ~ 42.6) and do the stem-and-leave display Do the stem and leaf display. Calculate the sample mean 39 40 41 42 43 44 45 46 4. Now we will use our knowledge of the value of the sample mean for this particular sample and the relationship between sample means (in general) and population mean (see questions 1 and 2 of this lab) to make an intelligent guess (estimation) of the population mean. Use the formula to calculate a 95 % confidence interval for the population mean (Show your work) ( , ) From the Minitab menu, use STAT>BASIC STATISTIC>ONE SAMPLE Z to check your calculations. Calculate the width of the confidence interval _______________ 5. Interpret the confidence interval you just found: We are 95% confident that the true mean processing time required to do a multiplication on a new 3-D computer lies between __________ and __________ microseconds. (The meaning of this is the following: Think of all the possible samples (all the possible sets of 16 multiplications) that we could have been done with this type of computer; 95% of those samples would have produced confidence intervals that contain the true mean, the other 5% would have been off)

## Lab on Confidence Intervals The story: Studies have shown that the random variable X, the processing time required to do a multiplication on a new 3-D computer, is normally distributed with mean and standard deviation 2 microseconds. A random sample of 16 observations is to be taken (i.e. 16 random multiplications will be performed and the time that it takes to perform each one of them will be annotated). The sample mean will be calculated. Part 1- The very basics 1. Before we collect the random sample, what can we say about the sampling distribution of ? 2. Before we collect the random sample, what is the probability that the sample mean will have a value that is greater than or equal to , and less than or equal to In other words, what is the probability that the sample mean is within 0.98 microseconds ( ) of the true (unknown) mean time? 3. A random sample was taken (i.e.16 multiplications were done) and the processing times were as follows: 42.65 45.15 39.32 44.44 41.63 41.54 41.59 45.68 46.50 41.35 44.37 40.27 43.87 43.79 43.28 40.70 Round the times to the nearest tenth (e.g. 42.65 ~ 42.6) and do the stem-and-leave display Do the stem and leaf display. Calculate the sample mean 39 40 41 42 43 44 45 46 4. Now we will use our knowledge of the value of the sample mean for this particular sample and the relationship between sample means (in general) and population mean (see questions 1 and 2 of this lab) to make an intelligent guess (estimation) of the population mean. Use the formula to calculate a 95 % confidence interval for the population mean (Show your work) ( , ) From the Minitab menu, use STAT>BASIC STATISTIC>ONE SAMPLE Z to check your calculations. Calculate the width of the confidence interval _______________ 5. Interpret the confidence interval you just found: We are 95% confident that the true mean processing time required to do a multiplication on a new 3-D computer lies between __________ and __________ microseconds. (The meaning of this is the following: Think of all the possible samples (all the possible sets of 16 multiplications) that we could have been done with this type of computer; 95% of those samples would have produced confidence intervals that contain the true mean, the other 5% would have been off)

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Normal time for a stopwatch study is equal to which of the following? Answer Average observed time × Performance rating factor Average observed time + Performance rating factor Average observed time / Performance rating factor Average observed time – Performance rating factor

## Normal time for a stopwatch study is equal to which of the following? Answer Average observed time × Performance rating factor Average observed time + Performance rating factor Average observed time / Performance rating factor Average observed time – Performance rating factor

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8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

## 8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

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