STA 2201 s 2011 Assignment Five:

Your written answers and printouts are due at the beginning of class Friday on March 18. You may be asked to present your solution to the class before handing it in.

For this assignment, we have two independent random samples from normal distributions, and the interest is in testing H0: σ21≤σ22 versus H1: σ21>σ22

  1. For n1=n2=50, suppose we obtain sample variances (with n-1 in the denominator) of s21=5.23 and s21=3.71. Calculate the F statistic and the p-value. Do you reject H0 at α=0.05?
  2. Explain why the power function of the F test is based on the central F distribution. Show a bit of calculation.
  3. What is the power of the F test at σ21=5 and σ22=4? The answer is a single number.
  4. Maintaining equal sample sizes, what total sample size is required for the test to have power of at lest 0.80 when σ21=5 and σ22=4? The answer is a single number.
  5. Consider a large-sample likelihood ratio test of the same null hypothesis. To compare, what is the approximate power of this test at σ21=5 and σ22=4? The answer is a single number.