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?