In Example 6.2, we use the computer to generate 1,000 samples, each containing n = 11…

In Example 6.2, we use the computer to generate 1,000 samples, each containing n = 11 observations, from a uniform distribution over the interval from 150 to 200. Now use the computer to generate 500 samples, each containing n = 15 observations, from that same population.

a. Calculate the sample mean for each sample. To approximate the sampling distribution of , construct a relative frequency histogram for the 500 values of .

b. Repeat part a for the sample median. Compare this approximate sampling distribution with the approximate sampling distribution of  found in part a.

Example 6.2

The rolling machine of a steel manufacturer produces sheets of steel of varying thickness. The thickness of a steel sheet follows a uniform distribution with values between 150 and 200 millimeters. Suppose we perform the following experiment over and over again: Randomly sample 11 steel sheets from the production line and record the thickness x of each. Calculate the two sample statistics

M = Median = Sixth sample measurement when the 11 thicknesses are arranged in ascending order

Obtain approximations to the sampling distributions of  and M.

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