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 $\bar { x } _ { 1 } = 7$ and $\bar { x } _ { 2 } = 11$, the sample standard deviations were $s _ { 1 } = 6$ and $s _ { 2 } = 4$, and the sample sizes were $n _ { 1 } = 10$ and $n _ { 2 } = 18$.
Compute the value of the test statistic.
A) -1.888
B) -4.411
C) -0.555
D) -2.935

Quizplus · Accepted Answer

The test statistic is:$$z = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} = \frac{7 - 11}{\sqrt{\frac{6^2}{10} + \frac{4^2}{18}}} = -1.888$$

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

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