1.An investor is concerned with the risk associated with a portfolio of stocks. He draws a random sample of nine monthly returns (expressed as a percentage of the initial investment). These data follow: 2, 5, -6, 10, 1, 2, -3, 0, and 7. Find a 95% confidence interval estimate of the population variance.

2.The grades of a sample of 10 applicants, selected at random from a large population, are 71, 86, 75, 63, 92, 70, 81, 59, 80, and 90. The professor claim that the grades variance is more than 123.

a.Compute the sample variance.

b.Test the hypothesis at 5% significance level.