Question

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A research analyst is examining a stock for possible inclusion in his client's portfolio. Over a 15-year period, the sample mean and the sample standard deviation of annual returns on the stock were 15% and 14%, respectively. The client wants to know if the risk, as measured by the standard deviation, differs from 12%. (You may find it useful to reference the appropriate table: chi-square table or F table)

a. Construct the 90% 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

Answer 1

Akat itial hst-td 썬 e.dafo, dla dand doraim can t ame 2. 2. 2 lyo. = 19,0556 OAS, (19.0336)

Please find your answer in the above images. For your reference I have also attached the Chi-Square table.

Steps for obtaining tabulated values.

1. First check degree of freedom(df) and level of significance($\alpha$).

2. In our case n=15 so df=n-1=14 and as we want to obtain 90% confidence interval , our $\alpha$=10%. Now, we need to check

$\chi ^{2}$ at df=14 and $\alpha$/2=0.05 for lower tail. (Column 6 and row no 14 will give us the value of same)= 6.571

and the $\chi ^{2}$ at df=14 and (1-$\alpha$/2)=0.95 for upper tail.(Column 3 and row no 14 will give us the desired value)= 23.685