2.15. Consider the computer output shown below.

Two-Sample T-Test and Cl: Y1, Y2 Two-sample T for Y1 vs Y2 N Mean Std. Dev. SE Mean Y1 20 50.19 1.71 0.38 Y2 20 52.52 2.48 0.55 Difference ! mu (X1) " mu (X2)

Estimate for difference: " 2.33341 95% CI for difference: (" 3.69547, " 0.97135)

T-Test of difference!0 (vs not !) : T-Value!"3.47 P-Value!0.001 DF!38 Both use Pooled Std. Dev. ! 2.1277

(a) Can the null hypothesis be rejected at the 0.05 level?

Why?

(b) Is this a one-sided or a two-sided test?

(c) If the hypotheses had been H0 : $1 ! $2 $ 2 versus H1 : $1 ! $2! 2 would you reject the null hypothesis at the 0.05 level?

(d) If the hypotheses had been H0 : $1 ! $2 $ 2 versus H1 : $1 ! $2 + 2 would you reject the null hypothesis at the 0.05 level? Can you answer this question without doing any additional calculations? Why?

(e) Use the output and the t table to find a 95 percent upper confidence bound on the difference in means.

(f) What is the P-value if the hypotheses are H0 : $1 !

$2 $ 2 versus H1: $1 ! $2 ! 2?