Tamara Hill,fund manager of the Hill Value Fund,manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio,i.e.,one with a price variance less than that of the S&P 500 index. Moreover,she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1)was 25,and for the last seven quarters the price variance for XYC common (population 2)was 8. Assume that stock prices are normally distributed in the population. Using $\alpha$ = 0.05,Tamara's alternate hypothesis is _______. A) $\sigma$₁² = $\sigma$₂² B) $\sigma$₁² $\neq$ $\sigma$₂² C) $\sigma$₁² $\sigma$₂² D) $\sigma$₁²

Question

Tamara Hill,fund manager of the Hill Value Fund,manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio,i.e.,one with a price variance less than that of the S&P 500 index. Moreover,she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1)was 25,and for the last seven quarters the price variance for XYC common (population 2)was 8. Assume that stock prices are normally distributed in the population. Using $\alpha$ = 0.05,Tamara's alternate hypothesis is _______. A) $\sigma$₁² = $\sigma$₂² B) $\sigma$₁² $\neq$ $\sigma$₂² C) $\sigma$₁² > $\sigma$₂² D) $\sigma$₁² < $\sigma$₂² E) s₁²< s₂²

Quizplus · Accepted Answer

The null hypothesis is that the variance of XYC common is greater than or equal to the variance of the S&P 500 index, while the alternate hypothesis is that the variance of XYC common is less than the variance of the S&P 500 index. Therefore, the appropriate test is a one-tailed test with a level of significance of 0.05. The formula for the F-test is F = s2(XYC) / s2(S&P 500), where s2(XYC) = 8 (the variance of XYC common) and s2(S&P 500) = 25 (the variance of the S&P 500 index). Plugging in the values, we get F = 8/25 = 0.32. The critical value of F at a level of significance of 0.05 with 249 and 248 degrees of freedom (the respective sample sizes minus 1) is 0.71. Since the calculated F-value is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the variance of XYC common is less than the variance of the S&P 500 index. Therefore, Tamara cannot add XYC common to the portfolio as a 'low risk' issue. The correct alternate hypothesis is that the variance of XYC common is greater than the variance of the S&P 500 index.

Tamara Hill,fund Manager of the Hill Value Fund,manages a Portfolio α\alphaα

Tamara Hill,fund Manager of the Hill Value Fund,manages a Portfolio $\alpha$