Question

The following null and alternative hypotheses have been stated: H0: µ1 - µ2 = 0 HA: µ1 - µ2 = ø to test the null hypothesis, random samples have been selected from the two normally distributed populations with equal variances. the following sample data were observed. sample from population 1: 33, 29, 35, 39, 39, 41, 25, 33, 38. sample from population 2: 46, 43, 42, 46, 44, 47, 50, 43, 39. the test null hypothesis using an alpha level equal to 0.05.

Answer 1

= 34.67

s1 = 5.24

= 44.44

s2 = 3.21

The pooled sample variance(s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2)

                                                      = (8 * (5.24)^2 + 8 * (3.21)^2)/(9 + 9 - 2)

                                                      = 18.88

The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

                             = (34.67 - 44.44)/sqrt(18.88/9 + 18.88/9)

                            = -4.77

DF = 9 + 9 - 2 = 16

At = 0.05, the critical values are t^* = +/- 2.120

Since the test statistic value is less than the lower critical value (-4.77 < -2.120), so we should reject the null hypothesis.