Use R to answer the following parts. Set the seed (order) of your randomizations by using the number 5065.
a) Create a matrix with 50 rows and 5 columns such that each row is a sample of size 5 from the exponential distribution with β=1. Print your matrix.
b) Compute the 90% t confidence intervals for the mean for each sample. Use a diagram or table to illustrate your intervals.
c) What percent of your intervals successfully captured the true mean?
d) Calculate the P-value for testing H0: β=1 vs. H1: β≠1 for each sample. Describe your P-values. Note that β is the mean of the exponential distribution. In how many tests did you reject H0? Use α=0.05.
e) The exponential distribution is a fairly extreme departure from normality. What can you conclude about the sensitivity of t intervals and tests to non-normality? This is, were the observed confidence level (for confidence interval) and significant level (for test) close to what you would expect?
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