6. Now use the histograms from Step 5 to answer the following questions:

a. Write a brief description of the shape, center, and spread for the histogram of the z values. Is what you see in the histogram consistent with what you would have expected to see? Explain. (Hint: In theory, what is the distribution of the z statistic?)

b. How does the histogram of the t values compare to the z histogram? Be sure to comment on center, shape, and spread.

c. Is your answer to Part

(b) consistent with what would be expected for a statistic that has a t distribution?

Explain.

d. The z and t histograms are based on only 200 samples, and they only approximate the corresponding sampling distributions. The 5th percentile for the standard normal distribution is 21.645 and the 95th percentile is 11.645. For a t distribution with df 5 5 2 1 5 4, the 5th and 95th percentiles are 22.13 and 12.13, respectively.

How do these percentiles compare to those of the distributions displayed in the histograms?

(Hint: Sort the 200 z values—in Minitab, choose

“Sort” from the Manip menu. Once the values are sorted, percentiles from the histogram can be found by counting in 10 [which is 5% of 200]

values from either end of the sorted list. Then repeat this with the t values.)

e. Are the results of your simulation and analysis consistent with the statement that the statistic z 5 x 2 m ss/Ïnd has a standard normal (z) distribution and the statistic t 5 x 2 m ss/Ïnd has a t distribution? Explain.