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LOS b: Formulate a null and an alternative hypothesis about the population value of a regression coefficient, calculate the value of the test statistic, determine whether to reject the null hypothesis at a given level of significance by using a one-tailed or two-tailed test, and interpret the results of the test.

An analyst is investigating the hypothesis that the beta of a fund is equal to one. The analyst takes 60 monthly returns for the fund and regresses them against the Wilshire 5000. The test statistic is 1.97 and the p-value is 0.05. Which of the following is CORRECT?

A)	If beta is equal to 1, the likelihood that the absolute value of the test statistic is equal to 1.97 is less than or equal to 5%.

B)	If beta is equal to 1, the likelihood that the absolute value of the test statistic would be greater than or equal to 1.97 is 5%.

C)	The proportion of occurrences when the absolute value of the test statistic will be higher when beta is equal to 1 than when beta is not equal to 1 is less than or equal to 5%.

A statistical test computes the likelihood of a test statistic being higher than a certain value assuming the null hypothesis is true.

David Black wants to test whether the estimated beta in a market model is equal to one. He collected a sample of 60 monthly returns on a stock and estimated the regression of the stock’s returns against those of the market. The estimated beta was 1.1, and the standard error of the coefficient is equal to 0.4. What should Black conclude regarding the beta if he uses a 5% level of significance? The null hypothesis that beta is:

A)	equal to one is rejected.

B)	equal to one cannot be rejected.

C)	not equal to one cannot be rejected.

The calculated t-statistic is t = (1.1 ? 1.0) / 0.4 = 0.25. The critical t-value for (60 ? 2) = 58 degrees of freedom is approximately 2.0. Therefore, the null hypothesis that beta is equal to one cannot be rejected.

Consider the following estimated regression equation, with standard errors of the coefficients as indicated:

The equation was estimated over 40 companies. Using a 5% level of significance, what are the hypotheses and the calculated test statistic to test whether the slope on R&D is different from 1.0?

A)	H₀: b_R&D = 1 versus H_a: b_R&D≠ 1; t = 0.556.

B)	H₀: b_R&D ≠ 1 versus H_a: b_R&D = 1; t = 2.778.

C)	H₀: b_R&D = 1 versus H_a: b_R&D≠1; t = 2.778.

The test for “is different from 1.0” requires the use of the “1” in the hypotheses and requires 1 to be specified as the hypothesized value in the test statistic. The calculated t-statistic = (1.25-1)/.45 = 0.556