Chapter 7, Problem 7.123ACB

Beta value of a stock. The “beta coefficient” of a stock is a measure of the stock’s volatility (or risk) relative to the market as a whole. Stocks with beta coefficients greater than 1 ·generally bear greater risk (more volatility) than the market, whereas stocks with beta coefficients less than 1 are less risky (less volatile) than the overall market (Alexander, Sharpe, and Bailey, Fundamentals of Investments, 2000). A random sample of 15 high-technology stocks was selected at the end of 2009, and the mean and standard deviation of the beta coefficients were calculated: x = 1.23, s = .37.

1. a. Set up the appropriate null and alternative hypotheses to test whether the average high-technology stock is riskier than the market as a whole.
2. b. Establish the appropriate test statistic and rejection region for the test. Use α = .10.
3. c. What assumptions are necessary to ensure the validity of the test?
4. d. Calculate the test statistic and state your conclusion.
5. e. What is the approximate p-value associated with this test? Interpret it.
6. f. Conduct a test to determine if the variance of the stock beta values differs from .15. Use α = .05.