In Example 4.27, we use the computer to generate 1,000 samples, each containing n= 11 obse...

In Example 4.27, 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 .

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

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

Simulating a Sampling Distribution—Thickness of Steel Sheets

Problem The rolling machine of a steel manufacturer produces sheets of steel of varying thickness. The thickness of a steel sheet ranges between 150 and 200 millimeters, with distribution shown in Figure.35. (This distribution is known as the uniform distribution.) 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

Obtain approximations to the sampling distributions of   and M.

Solution We used MINITAB to generate 1,000 samples from this population, each with n= 11 observations. Then we computed   and M for each sample. Our goal is to obtain approximations to the sampling distributions of   and M in order to find out which sample statistic ( or M) contains more information about m. [Note: In this particular example, it is known that the population mean is μ = 175 mm.] The first 10 of the 1,000 samples generated are presented in Table.10. For instance, the first computer generated sample from the uniform distribution contained the following measurements (arranged in ascending order): 151, 157, 162, 169, 171, 173, 181, 182, 187, 188, and 193 millimeters. The sample mean   and median M computed for this sample are