Velma Vasquez,fund manager of the Vasquez Value Fund,manages a portfolio of 250 common stocks. Velma relies on various statistics,such as variance,to assess the overall risk of stocks in an economic sector.Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%. Assume that annualized returns are normally distributed. The 95% confidence interval for the population variance of annualized returns is _______.
A) 0.018 to 0.064
B) 0.016 to 0.078
C) 0.017 to 0.066
D) 0.016 to 0.075
E) 0.020 to 0.080

Question

Quizplus · Accepted Answer

The confidence interval for the population variance is calculated using the chi-square distribution. With 14 samples, the degrees of freedom is 13. Using the chi-square distribution table, the 95% confidence interval for the variance is calculated as (13 * 3) / chi-square value at 97.5% and (13 * 3) / chi-square value at 2.5%, which results in the interval 0.016 to 0.078.

Velma Vasquez,fund Manager of the Vasquez Value Fund,manages a Portfolio