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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 regression model. In this case, the p-value for the F-statistic is 0.045, which is less than the significance level of 0.05. This indicates that at least one of the independent variables (in this case, the average years of experience per employee) has a statistically significant effect on the dependent variable (corporate revenue). Therefore, the analyst can reject the joint null hypothesis that both β1 and β2 are equal to zero. The t-tests for β1 and β2 individually have p-values of 0.07 and 0.06, respectively, which are greater than the 95% confidence level threshold of 0.05. This means that we cannot reject the null hypothesis for either β1 or β2 individually. However, the joint hypothesis test using the F-statistic takes into account the combined effect of all the independent variables, and in this case, it is significant, allowing the analyst to reject the joint null hypothesis.
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In a study involving 400 different companies, the relationship between total corporate earnings () and the average tenure of experience for each worker () is modeled using the following regression equation: where ranges from 1 to 400. The goal of the research is to test the joint null hypothesis that both and at a 95% confidence level. The p-value derived from the t-statistic for is 0.07, the p-value for the t-statistic for is 0.06, and the p-value from the F-statistic for the overall 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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