7.28 Central limit theorem for uniform population Let’s use the Sampling Distribution of the Sample Mean web app accessible from the book’s website to show that the first population distribution shown in Figure 7.11 has a more nearly normal sampling distribution for the mean as n increases. Select uniform for the population distribution and keep the default settings of 0 and 1 for the lower and upper bound.

a. Use the app to simulate the sampling distribution when the sample size n = 2. Run 10,000 simulations and look at the resulting histogram of the sample means. (You may want to decrease the binsize a bit to get a clearer picture.) What shape does the simulated sampling distribution have?

b. Repeat part

a, but now use a sample size of n = 5.

Explain how the variability and the shape of the simulated sampling distribution changes as n increases from 2 to 5.

c. Repeat part

a, but now use a sample size of n = 30.

Explain how the variability and the shape of the simulated sampling distribution changes as n increases from 2 to 30. Compare results from parts a-c to the first column of Figure 7.11.

d. Explain how the central limit theorem describes what you have observed.