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Mathematics, 24.03.2020 01:36 macybarham
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 the greater risk (more volatility) than the market, whereas stocks with beta coefficients less than 1 are less risky (less volatile) than the overall market. A random sample of 15 high-technology stocks was selected at the end of 2009, and the sample mean and sample standard deviation of the beta coefficients were computed to be 1.23 and s=.37, respectively. (Assume that the beta coefficient follows a normal distribution.)
a. State the null and alternative hypothesis to test whether the average high-technology stock is riskier than the market as a whole.
b. Establish the appropriate test statistics for this problem.
c. Determine an appropriate decision rule for testing the hypothesis in part a at the level of significance α = .01.
d. Make an appropriate conclusion based on the summary statistics provided in the problem and the decision rule you specified in part c.
e. What is the p-value of the test.
f. Based on the p-value calculated in part (e), do you reject the null hypothesis at the level of significance α=.01? Say how you made your decision.
g. How does your conclusion change if instead of α=.01 we chose a smaller level of significance? Explain.
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