Homework 1: 1.25, 1.34, 1.43, 1.54, 1.60, 1.63, 1.74, 1.77, 1.79, 1.81 (due Friday 1/18)
In addition the following problem:
Carry out a simulation experiment using MINITAB (see details
below) to study the sampling distribution of the sample mean when the
population is:
a. Uniform on the interval (0,1)
b. Exponential with mean 1.
Consider in each case three sample sizes n = 5, 20 and 100 and
use k = 500 replications. Discuss your findings (in the spirit of
examples 5.22 and 5.23 in the book), compare the results for the two
populations and relate them to the central limit theorem.
Using Minitab for windows for the simulation experiment:
1. Generating the random samples:
Calc -> random data -> (specify distribution, uniform or exponential)
generate 500 raws of data (k=500 the number of random samples)
store in columns C1-C5 (for sample size n=5 and similarly for n=20 or 100)
specify the parameters of the distribution
2. Calculate the statistic:
Calc -> Row statistics
specify statistic of interest (mean for the problem)
input variables C1-C5
store result in C6
Finally, C6 contains 500 realizations from the sampling distribution of the sample mean when n=5. Obtain a histogram (Graph -> Histogram) and numerical measures (Stat -> basic statistics -> display descriptive statistics) to summarize this sampling distribution.