6. Two random samples from two normal populations, means 1 and 2, and with standard deviations 1 = 4.5 and 2 = 6.2, respectively, produced

6. Two random samples from two normal populations, means μ1 and μ2, and with standard deviations σ1 = 4.5 and σ2 = 6.2, respectively, produced the following data:

Sample I 40 26 37 44 25 35 35 43 39 29 34 43 34 42 29 38 Sample II 51 40 29 47 43 36 47 38 40 26 26 38 37 27 34 35

(a) Test at the 2% level of significance the hypothesis H0: μ1 − μ2 = 0 versus H1: μ1 − μ2 = 0.

(b) Find the p-value for the test and make your conclusions using the p-value. Do you arrive at the same conclusion as in (a)?