Question: A laboratory is doing a quality assurance study of its performance. In a test of its measurement of serum cholesterol, 15 samples containing the same known amount of cholesterol (190 mg/dL) of serum cholesterol are submitted for measurement as part of a larger batch of samples, one sample each day over a three week period. Suppose that following daily values in mg/DL for serum cholesterol were obtained for these 15 samples

a. (5 points) Assume that the variance 2σ for the measurement of serum cholesterol is supposed to be no larger than 100. Construct a 95% confidence interval estimate of the unknown true variance. You may assume that the 15 measurements are a simple random sample from a normal distribution. 2σ

b. Have a look at the confidence interval that you constructed in answering question #2a. Does it include the value of 100? In 1-2 sentences, interpret the confidence interval you obtained.