Suppose that (Y₁, X;) satisfy the assumptions specified here. A random sample of n = 280 is drawn and yields = 8.69 + 4.

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Suppose That Y X Satisfy The Assumptions Specified Here A Random Sample Of N 280 Is Drawn And Yields 8 69 4 1 (100.79 KiB) Viewed 31 times

Suppose that (Y₁, X;) satisfy the assumptions specified here. A random sample of n = 280 is drawn and yields = 8.69 + 4.89X, R² = 0.75, SER = 4.3 (4.2) (4.8) Where the numbers in parentheses are the standard errors of the estimated coefficients = 8.69 and ₁ Suppose you wanted to test that B₁ is zero at the 5% level. That is, Report the t-statistic and p-value for this test. Based on the p-value computed above, would you reject the null hypothesis at the 5% level? A. No B. Yes = 4.89 respectively. Ho: B₁ = 0 vs. H₁: B₁ #0 The t-statistic is (Round your response to two decimal places) The p-value is (Round your response to two decimal places)

Construct a 95% confidencen interval for ₁. Supposed you learned that Y; and X; were independent. Would you be surpised? The 95% confidence interval for B₁ is (Round your response to two decimal places) A. No, I wouldn't be surprised because the null hypothesis that B₁ is zero was not rejected at the 5% significance level. B. No, I wouldn't be surprised because the null hypothesis that B₁ is zero was rejected at the 5% significance level. C. Yes, I would be surprised because the null hypothesis that B₁ is zero was rejected at the 5% significance level. D. Yes, I would be surprised because the null hypothesis that B₁ is zero was not rejected at the 5% significance level. Suppose that Y, and X; are independent and many samples of size n = 280 are drawn and regressions estimated. Suppose that you test the null hypothesis that B₁ is zero at the 5% level and construct a 95% confidence interval for ₁. In what fraction of the samples would the null hypothesis that ₁ is zero at the 5% level be rejected? A. The null hypothesis would be rejected in 5% of the samples. B. The null hypothesis would be rejected in 90% of the samples. C. The null hypothesis would be rejected in 95% of the samples. D. The null hypothesis would be rejected in 10% of the samples.

In what fraction of the samples would the value ₁ = 0 be included in the 95% confidence interval for B₁q? = 0. A. 90% of the confidence intervals would contain the value ₁ B. 10% of the confidence intervals would contain the value ₁ = 0. = 0. C. 95% of the confidence intervals would contain the value ₁ D. 5% of the confidence intervals would contain the value B₁ = 0.