Examine the sample obtained from a normally distributed population:

5.2 10.4 5.1 2.1 4.8 15.5 10.2 8.7 2.8 4.9 4.7 13.4 15.6 14.5

a. Calculate the variance.

b. Calculate the probability that a randomly chosen sample would produce a sample variance at least as large as that produced in part a if the population variance was equal to 20.

c. What is the statistical term used to describe the probability calculated in part b?

d. Conduct a hypothesis test to determine if the population variance is larger than 15.3. Use a significance level equal to 0.05.