A research analyst is examining a stock for possible inclusion in his client's portfolio. Over a 10-year period, the sample mean and the sample standard deviation of annual returns on the stock were 20% and 15%, respectively. The client wants to know if the risk, as measured by the standard deviation, differs from 18%. (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.)

	Confidence Intervals
Population Variance	_ to _
Population Standard Deviation	_ to _

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

multiple choice 1

• 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 18%?

multiple choice 2

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