50. Two random samples from two normal populations with standard deviations 1 = 4.5 and 2 = 6.2, respectively, produced the following data: Sample from

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

Sample from population I 20 30 31 28 34 35 32 26 24 38 25 40 Sample from population II 34 36 49 52 41 44 30 33 47 49 39

(a) Test at the 2% level of significance the hypothesis Ho : 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)?