Suppose you want to test the claim that $\mu _ { 1 }

Question

Suppose you want to test the claim that $\mu _ { 1 } < \mu _ { 2 }$ 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: $\sigma _ { 1 } = 2.9 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\overline { \mathrm { x } } 1 = 28.85 , \mathrm { n } _ { 1 } = 35 \text { and } \overline { \mathrm { x } } 2 = 31.4 , \mathrm { n } _ { 2 } = 42$
A)Reject H₀ if the standardized test statistic is less than -1.645.
B)Reject H₀ if the standardized test statistic is less than -1.96.
C)Reject H₀ if the standardized test statistic is less than -2.33.
D)Reject H₀ if the standardized test statistic is less than -2.575.

Quizplus · Accepted Answer

Given the significance level $\alpha = 0.05$ and the directional nature of the hypothesis test ($\mu_1 < \mu_2$), a one-tailed test is appropriate. For a one-tailed test at $\alpha = 0.05$, the critical value from the Z-distribution is -1.645. Therefore, you would reject $H_0$ if the standardized test statistic is less than -1.645.

Suppose You Want to Test the Claim That μ1<μ2\mu _ { 1 } < \mu _ { 2 }μ1​<μ2​

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