Suppose that (Y,- Xi) satisfy the assumptions specified here. A random sample of n = 457 is drawn and yields Tr: 9.49 + 3.77X, R2 = 0.53, SER = 6.6 (2.3) (3.2) Where the numbers in parentheses are the standard errors of the estimated coefficients 230 = 9.49 and ,31 = 3.77 respectively. Suppose you wanted to test that [31 is zero at the 5% level. That is. H0:1 =0 vs. H1: ,61 #0 Report the tstatistic and pvalue for this test. The tstatistic is 1.18 . (Round your response to two decimal places) The pvalue is 024'. (Round your response to two decimal places) Based on the pvalue computed above, would you reject the null hypothesis at the 5% level? x Yes No Construct a 95% condencen interval for m . The 95% condence interval for m is [ 2.5o', 10.04'] (Round your response to two decimal places) Supposed you learned that Y, and X,- were independent. Would you be surpised'? Yes, I would be surprised because the null hypothesis that [91 is zero was not rejected at the 5% significance level. No, I wouldn't be surprised because the null hypothesis that [91 is zero was not rejected at the 5% significance level. No, I wouldn't be surprised because the null hypothesis that [91 is zero was rejected at the 5% significance level. Yes, I would be surprised because the null hypothesis that [91 is zero was rejected at the 5% significance level. Suppose that Y,- and X,- are independent and many samples of size n = 457 are drawn and regressions estimated. Suppose that you test the null hypothesis that 1 is zero at the 5% level and construct a 95% condence interval for m. In what fraction of the samples would the null hypothesis that ,51 is zero at the 5% level be rejected? The null hypothesis would be rejected in 90% of the samples. The null hypothesis would be rejected in 95% of the samples. The null hypothesis would be rejected in 5% of the samples. The null hypothesis would be rejected in 10% of the samples. In what fraction of the samples would the value A = 0 be included in the 95% confidence interval for/91? V 95% of the condence intervals would contain the value A = 0. 5% of the confidence intervals would contain the value [91 = 0. 90% of the condence intervals would contain the value 1 = 0. 10% of the condence intervals would contain the value 1 = 0