Find the standardized test statistic to test the claim that $\mu _ { 1 } \mu _ { 2 } .$ Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 45 \text { and } \sigma _ { 2 } = 25$ Sample statistics: $\bar { x } 1 = 480 , n _ { 1 } = 100 \text { and } \bar { x } { 2 } = 465 , n _ { 2 } = 125$
A)2.99
B)2.81
C)1.86
D)0.91

Question

Find the standardized test statistic to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 45 \text { and } \sigma _ { 2 } = 25$ Sample statistics: $\bar { x } 1 = 480 , n _ { 1 } = 100 \text { and } \bar { x }  { 2 } = 465 , n _ { 2 } = 125$
A)2.99
B)2.81
C)1.86
D)0.91

Quizplus · Accepted Answer

The standardized test statistic for comparing two means with known population standard deviations is given by the formula: $$Z = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$ Plugging in the given values: $$Z = \frac{480 - 465}{\sqrt{\frac{45^2}{100} + \frac{25^2}{125}}} = \frac{15}{\sqrt{\frac{2025}{100} + \frac{625}{125}}} = \frac{15}{\sqrt{20.25 + 5}} = \frac{15}{\sqrt{25.25}} = \frac{15}{5.025} \approx 2.99.$$

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 $\mu _ { 1 } > \mu _ { 2 } .$