Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \stackrel { 2 } { 1 } \neq \sigma _ { 2 } ^{ 2 }$ $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 515 & \overline { \mathrm { x } _ { 2 } } = 500 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A)1.282
B)3.271
C)2.819
D)1.865

Question

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \stackrel { 2 } { 1 } \neq \sigma _ { 2 } ^{ 2 }$ $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 515 & \overline { \mathrm { x } _ { 2 } } = 500 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A)1.282
B)3.271
C)2.819
D)1.865

Quizplus · Accepted Answer

The correct choice is A because the standardized test statistic, t, is calculated as:$$t = \frac{(\overline{x}_1 - \overline{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$$Plugging in the given values, we get:$$t = \frac{(515 - 500) - (0 - 0)}{\sqrt{\frac{40^2}{18} + \frac{25^2}{13}}} = 1.282$$

Find the Standardized Test Statistic, T, to Test the Claim μ1>μ2.\mu _ { 1 } > \mu _ { 2 } .μ1​>μ2​.

Find the Standardized Test Statistic, T, to Test the Claim $\mu _ { 1 } > \mu _ { 2 } .$