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.

She checks a particular motel for the number of rooms rented. She chooses 20 randomly selected dates in December and early January to examine the occupancy records for those dates. From her collected data, she found a standard deviation of 3.86 rooms rented. If the number of rooms rented is normally distributed, find the 95% confidence interval for the population standard deviation of the number of rooms rented.
Write a conclusion for your finding.