Question

A research analyst is examining a stock for possible inclusion in his client's portfolio. Over a 17-year period, the sample mean and the sample standard deviation of annual returns on the stock were 18% and 15%, respectively. The client wants to know if the risk, as measured by the standard deviation, differs from 17%. (You may find it useful to reference the appropriate table: chi-square table or F table)

a. Construct the 95% confidence intervals for the population variance and the population standard deviation. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

b. What assumption did you make in constructing the confidence intervals?

• Annual return is not necessarily normally distributed.

• Annual return is normally distributed

c. Based on the above confidence intervals, can we state that the risk differs from 17%?

• Yes, since the confidence interval does not include the hypothesized value.

• No, since the confidence interval includes the hypothesized value.

• No, since the confidence interval does not include the hypothesized value.

• Yes, since the confidence interval includes the hypothesized value.

Answer 1