Suppose that left parenthesis Upper Y Subscript i comma Upper X Subscript i right parenthesis satisfy the assumptions specified here.

. A random sample of n = 297 is drawn and yields ModifyingAbove Upper Y with caret equals6.54+5.51X,Upper R squared= 0.02, SER = 8.3(4.1)(3.1)

Where the numbers in parentheses are the standard errors of the estimated coefficients

ModifyingAbove beta with caret 0 equals 6.54 and ModifyingAbove beta with caret 1 equals 5.51 respectively. Suppose you wanted to test that beta 1 is zero at the 5% level. That is, Upper H 0 : beta 1 equals 0 vs. Upper H 1 : beta 1 not equals 0 Report the t-statistic and p-value for this test.The t-statistic is nothing.

compute The p-value and explain all step (show a picture of t table in nedeed) ?

Based on the p-value computed above, would you reject the null hypothesis at the 5% level?

A.

No

B.

Yes

Construct a 95% confidencen interval for beta 1.

The 95% confidence interval for beta 1 is? [ , ]

Supposed you learned that Upper Y Subscript i and Upper X Subscript i were independent. Would you be surpised?

A.

Yes, I would be surprised because the null hypothesis that beta 1 is zero was rejected at the 5% significance level.

B.

No, I wouldn't be surprised because the null hypothesis that beta 1 is zero was not

rejected at the 5% significance level.

C.

No, I wouldn't be surprised because the null hypothesis that

beta 1 is zero was rejected at the 5% significance level.

D.

Yes, I would be surprised because the null hypothesis that beta 1 is zero

was not rejected at the 5% significance level.

Suppose that Upper Y Subscript i and Upper X Subscript i are independent and many samples of size n = 297 are drawn and regressions estimated. Suppose that you test the null hypothesis that beta 1 is zero at the 5% level and construct a 95% confidence interval for beta 1.

In what fraction of the samples would the null hypothesis that beta 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 10% of the samples.

D.

The null hypothesis would be rejected in 95% of the samples.

In what fraction of the samples would the value beta 1 = 0 be included in the 95% confidence interval for beta 1 ?

A.

90% of the confidence intervals would contain the value

beta 1= 0.

B.

10% of the confidence intervals would contain the value

beta 1= 0.

C.

5% of the confidence intervals would contain the value

beta 1= 0.

D.

95% of the confidence intervals would contain the value

beta 1= 0.