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Answer: The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level.
The correct answer is C. The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level. The F-statistic is used to test the joint significance of all the independent variables in a multiple regression model. In this case, the F-statistic has a p-value of 0.045, which is less than the significance level of 0.05. This indicates that at least one of the independent variables has a significant effect on the dependent variable, and thus, the joint null hypothesis that β1 = 0 and β2 = 0 can be rejected. The individual t-tests for β1 and β2 are not sufficient to test the joint hypothesis, as they have p-values of 0.07 and 0.06, respectively, which are greater than the significance level of 0.05. Therefore, the correct conclusion is that the analyst can reject the joint null hypothesis based on the significance of the F-statistic.
Author: LeetQuiz Editorial Team
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In a study analyzing data from 400 companies, the relationship between a company's total earnings (Yi) and the average number of years of experience of its workers (Xi) is modeled by the following linear regression equation: Yi = β1 + β2 * Xi + Ei for i = 1, 2, ..., 400 A financial analyst aims to test the joint null hypothesis that both coefficients β1 and β2 are equal to zero, at a 95% confidence level. The p-value associated with the t-statistic for β1 is 0.07, the p-value associated with the t-statistic for β2 is 0.06, and the p-value for the F-statistic of the overall regression model is 0.045.
A
The analyst can reject the joint null hypothesis because each β is different from 0 at the 95% confidence level.
B
The analyst cannot reject the joint null hypothesis because neither β is different from 0 at the 95% confidence level.
C
The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level.
D
The analyst cannot reject the joint null hypothesis because the F-statistic is not significant at the 95% confidence level.
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