A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ versus $H _ { 1 } : \mu _ { 1 }

Question

A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ versus $H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }$. The sample means were $\bar { x } _ { 1 } = 11$ and $\bar { x } _ { 2 } = 9$, the sample standard deviations were $s _ { 1 } = 7$ and $s _ { 2 } = 5$, and the sample sizes were $n _ { 1 } = 15$ and $n _ { 2 } = 13$.
Is $H _ { 0 }$ rejected at the $0.05$ level? (Hint: First compute the value of the test statistic.)
A) No
B) Yes

Quizplus · Accepted Answer

The test statistic for comparing two means (assuming unequal variances) is given by $t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$. Substituting the given values, we find that the test statistic does not exceed the critical value for rejecting $H_0$ at the 0.05 level, especially since $\bar{x}_1 < \bar{x}_2$, which contradicts the alternative hypothesis $H_1: \mu_1 < \mu_2$.

A Test Was Made Of H0:μ1=μ2H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }H0​:μ1​=μ2​

A Test Was Made Of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$