Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Assume the two samples are random and independent. At a level of significance of α $\alpha$ = 0.05, when should you reject H₀?
Population statistics: $\sigma _ { 1 } = 1.5 \text { and } \sigma _ { 2 } = 1.9$ Sample statistics: $\overline { \mathrm { x } } 1 = 19 , \mathrm { n } _ { 1 } = 50 \text { and } \overline { \mathrm { x } } 2 = 17 , \mathrm { n } _ { 2 } = 60$
A)Reject H₀ if the standardized test statistic is less than -1.96 or greater than 1.96.
B)Reject H₀ if the standardized test statistic is less than -2.33 or greater than 2.33.
C)Reject H₀ if the standardized test statistic is less than -1.645 or greater than 1.645.
D)Reject H₀ if the standardized test statistic is less than -2.575 or greater than 2.575.

Question

Quizplus · Accepted Answer

Given the level of significance $\alpha = 0.05$ and the fact that the test is two-tailed (since we're testing $\mu_1 \neq \mu_2$), the critical values for rejection of $H_0$ correspond to the z-scores that cut off the outer 5% of the standard normal distribution, split into 2.5% in each tail. The z-scores that correspond to these cutoffs are approximately $\pm1.96$.

Suppose You Want to Test the Claim That μ1≠μ2.\mu _ { 1 } \neq \mu _ { 2 } .μ1​=μ2​.

Suppose You Want to Test the Claim That $\mu _ { 1 } \neq \mu _ { 2 } .$