Question

Consider the following hypothesis test. The following results are for two independent samples taken from the two populations. Sample 2 n2=70 X 2 106 7.6 Sample 1 1-104 7 1 -8.4 a. What is the value of the test statistic? If required enter negative values as negative numbers (to 2 decimals). b. What is the p-value (to 4 decimals)? Use z-table. C. With α-.05, what is your hypothesis testing conclusion? Select Icon Key

Answer 1

Given that,

$n_1 = 80, \bar x_1 = 104, \sigma_1 = 8.4$

$n_2 = 70, \bar x_2 = 106, \sigma_2 = 7.6$

The null and the alternative hypotheses are,

$H_0: \mu_1 - \mu_2 =0$

$H_a: \mu_1 - \mu_2 \neq 0$

a) Test statistic is,

$Z = \frac {\bar x_1 - \bar x_2} {\sqrt { \frac {\sigma_1^2}{n_1} + \frac {\sigma_2^2}{n_2}}} = \frac {104 - 106}{\sqrt { \frac {(8.4)^2}{80} + \frac {(7.6)^2}{70}}} = -1.53$

Test statistic = -1.53

b) p-value = 2 * P(Z < -1.53) = 2 * 0.0630 = 0.1260

=> p-value = 0.1260

c) Since, p-value = 0.1260 > $\alpha = 0.05$

We fail to reject the null hypothesis ( H₀ ).