Suppose you want 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 $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ At a
Level of significance of α $\alpha = 0.05$ when should you reject H₀? $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \
\overline { \mathrm { x } } _ { 1 } = 21 & \overline { \mathrm { x } _ { 2 }} = 22 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A)Reject H₀ if the standardized test statistic is less than -2.064 or greater than 2.064.
B)Reject H₀ if the standardized test statistic is less than -2.492 or greater than 2.492
C)Reject H₀ if the standardized test statistic is less than -1.711 or greater than 1.711.
D)Reject H₀ if the standardized test statistic is less than -1.318 or greater than 1.318.

Question

Suppose you want 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 $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ At a
Level of significance of α $\alpha = 0.05$ when should you reject H₀? $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \
\overline { \mathrm { x } } _ { 1 } = 21 & \overline { \mathrm { x } _ { 2 }} = 22 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A)Reject H₀ if the standardized test statistic is less than -2.064 or greater than 2.064.
B)Reject H₀ if the standardized test statistic is less than -2.492 or greater than 2.492
C)Reject H₀ if the standardized test statistic is less than -1.711 or greater than 1.711.
D)Reject H₀ if the standardized test statistic is less than -1.318 or greater than 1.318.

Quizplus · Accepted Answer

Given the sample sizes, the degrees of freedom for the two-sample t-test can be approximated using the smaller of $n_1 - 1$ and $n_2 - 1$, which are 13 and 11, respectively. Therefore, we use 11 degrees of freedom for a conservative estimate. At a significance level of $\alpha = 0.05$ and with two tails, we look up the critical value in the t-distribution table for 11 degrees of freedom, which is approximately 2.064. This means we reject $H_0$ if the test statistic is beyond these critical values in either direction.

Suppose You Want to Test the Claim That μ1=μ2.\mu _ { 1 } = \mu _ { 2 } .μ1​=μ2​.

Suppose You Want to Test the Claim That $\mu _ { 1 } = \mu _ { 2 } .$