Bootstrap versus sampling distribution. Most statistical software includes a function to generate samples from Normal distributions. Set the mean to 8.4 and the standard deviation to 14.7. You can think of all the numbers that would be produced by this function if it ran forever as a population that has the N(8.4, 14.7) distribution. Samples produced by the function are samples from this population.
(a) What is the exact sampling distribution of the sample mean x for a sample of size n from this population?
(b) Draw an SRS of size n = 10 from this population. Bootstrap the sample mean x using 1000 resamples from your sample. Give a histogram of the bootstrap distribution and the bootstrap standard error.
(c) Repeat the same process for samples of sizes n = 40 and n = 160.
(d) Write a careful description comparing the three bootstrap distributions and also comparing them with the exact sampling distribution. What are the effects of increasing the sample size?