Find the standardized test statistic to test the claim that $\mu _ { 1 } = \mu _ { 2 }$ . Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 2.5 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\overline { \mathrm { x } } 1 = 3 , \mathrm { n } _ { 1 } = 40 \text { and } \overline { \mathrm { x } } 2 = 4 , \mathrm { n } _ { 2 } = 35$
A)-1.6
B)-0.8
C)-2.6
D)-1.0

Question

Quizplus · Accepted Answer

The standardized test statistic is:$$z = \frac{(\overline{x}_1 - \overline{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$Plugging in the given values, we get:$$z = \frac{(3 - 4) - (0 - 0)}{\sqrt{\frac{2.5^2}{40} + \frac{2.8^2}{35}}} = -1.6$$Therefore, the correct choice is A.

Find the Standardized Test Statistic to Test the Claim That μ1=μ2\mu _ { 1 } = \mu _ { 2 }μ1​=μ2​

Find the Standardized Test Statistic to Test the Claim That $\mu _ { 1 } = \mu _ { 2 }$