Tamara Hill, Fund Manager of the Hill Value Fund, Manages $\alpha$

Multiple Choice

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, the appropriate decision is _______.

A) reject the null hypothesis $\sigma$ ₁ ²= $\sigma$ ₁ ²
B) reject the null hypothesis $\sigma$ ₁ ² $\neq$$\sigma$ ₁ ²
C) do not reject the null hypothesis $\sigma$ ₁ ² $\le$ $\sigma$ ₂ ²
D) do not reject the null hypothesis $\sigma$ ₁ ² $\neq$ $\sigma$ ₁ ²
E) do nothing