Consider the particle size of a particular product. The product specifications require that the variance of the particle sizes be 14.40. Production personnel measured the particle size for a sample of 25 observations, with the following results:
99.6 92.1 103.8 95.3 101.6
102.8 100.9 100.5 102.7 96.9
101.5 96.7 96.8 97.8 104.7
103.2 97.5 98.3 105.8 100.6
102.3 93.8 102.7 94.9 94.9
a. Conduct a hypothesis test to test the claim that the variance of the particle sizes is 14.40. Use an α=0.05.
b. Construct a 95% confidence interval for the true variance of the particle sizes.
c. What assumptions did you have to make in order to perform the above analyses? Please evaluate how well the data meet the assumptions.