To be done using R:

9. Student's-T distribution. a. Please simulate 4 independent random numbers from the standard normal distribution. Calculate the sample mean and sample standard deviation. Report T =- s/14 Repeat the simulation 100 times and draw a histogram for T. b. Report the 5%, 10%, 50%, 90%, and 95% percentiles of the 100 T values. Compare them with the table A.4 on page 496 in the row of "df=3". C. Please generate 100 random samples of size 30 from N(1,4). (Generate 30 random numbers, and repeat the generation 100 times.) Calculate - 1 T=130 and plot the histogram of T. Report the 5%, 10%, 50%, 90%, and 95% percentiles of the 100 T values