8.46 Simulating the confidence interval Go to the Inference for a Mean web app, accessible on the book’s website. Select the Explore Coverage tab and keep the default skewed shape for the population distribution as well as the default confidence level of 95%. Set the sample size to 30 and generate 100 random samples by selecting 100 and clicking on Draw Sample(s). The graph will now show 100 confidence intervals for m, based on 100 generated sample from the population distribution.

a. How many of the intervals you generated fail to contain the population mean m = 14.3?

b. How many would you expect not to contain the true value?

c. Now repeat the simulation using at least 1000 random samples of size 30. Why do close to 95% of the intervals contain m, even though the population distribution is quite skewed?