Question

22) Suppose you want to test the claim that μ1 > μ2. Two samples are randomly selected from each population. The sample statistics are given below. At a level of significance of α = 0.10, find the test statistic and determine whether or not to reject H0. (8.1) n1 = 35 n2 = 42 x1 = 33 x2 = 31 s1 = 2.9 s2 = 2.8

A) z = 3.06; Reject H0 and support the claim that μ1 > μ2 B) z = -3.06; Reject H0 and support the claim that μ1 > μ2 C) z = 3.06; Fail to Reject H0 and we do not support the claim that μ1 > μ2 D) z = -3.06; Fail to Reject H0 and we do not support the claim that μ1 > μ2

Answer 1

Given that, the null and alternative hypotheses are,

H0 : μ1 = μ2

Ha : μ1 > μ2

Test statistic is,

$Z = \frac { \bar x_1 -\bar x_2}{\sqrt {\frac { s_1^2}{n_1} +\frac {s_2^2}{n_2}}} = \frac { 33-31}{\sqrt {\frac {(2.9)^2}{35} +\frac {(2.8)^2}{42}}} = 3.06$

p-value = P(Z > 3.06) = 0.0011

Since, p-value = 0.0011 < 0.10, we reject the null hypothesis.

Answer : A) z = 3.06; Reject H0 and support the claim that μ1 > μ2