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 \((190 \mathrm{mg} / \mathrm{dL})\) 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 \(\mathrm{mg} / \mathrm{DL}\) for serum cholesterol were obtained for these 15 samples

1. Assume that the variance \(\sigma^{2}\) 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.
2. 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.

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