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?
This question was asked on Jul 20, 2016 and answered on Jul 22, 2016.
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