A create a matrix with 50 rows and 5 columns such that

Question

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 ß=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: ß=1 vs. H₁: ß?1 for each sample. Describe your P-values. Note that ß is the mean of the exponential distribution. In how many tests did you reject H₀? Use a=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?