THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 8 households was asked about their monthly income (x) and the number of hours they spend connected to the internet each month (y) .The data yield the following statistics:
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,
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-Which of the following is the value of the test statistic for testing H₀ : β₁ = 0 vs.H₁ : β₁ ≠ 0?

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 8 households was asked about their monthly income (x) and the number of hours they spend connected to the internet each month (y) .The data yield the following statistics:

,

-Which of the following is the value of the test statistic for testing H₀ : β₁ = 0 vs.H₁ : β₁ ≠ 0?

Quizplus · Accepted Answer

To test the null hypothesis β = 0, we use the t-test. The test statistic for β₁ is calculated as: t = (β₁ - 0)/SE(β₁) where SE(β₁) is the standard error of the estimate for β₁. From the output provided, we can see that the estimate for β₁ is 0.4055 and the standard error of the estimate is 0.1711. Substituting these values into the formula for the t-test statistic, we get: t = (0.4055 - 0)/0.1711 = 2.3660 This corresponds to a p-value of 0.0469, which is less than the standard significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence of a nonzero relationship between monthly income and internet usage. The best choice(s) is B) only, as it correctly identifies the test statistic and its value.