Question

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 35% and 13%, respectively. The client wants to know if the risk, as measured by the standard deviation, differs from 30%. Use Table 3.

  

a.	Construct the 95% confidence intervals for the population variance and the population standard deviation. (Round your answer to 2 decimal places.)

  

	Confidence Interval
Population variance	to
Population standard deviation	to

  

b.	What assumption did you make in constructing the confidence interval?
	Annual return is normally distributed Annual return is not necessarily normally distributed

  

c.	Based on the above confidence interval, can we state that the risk differs from 30%?
	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

a.

The confidence interval of variance would be given by,

The degree of freedom in this case would be given by,

df = n - 1 = 10 - 1 = 9

The critical values would be given by,

Hence the confidence interval for population variance would be given by,

The confidence interval for population standard deviation is given by,

Hence the confidence interval in this case would be given by,

b.

The correct option would be ,

Annual return is normally distributed

c.

Since the hypothesized value does not lie in the confidence interval , the correct option would be,

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