Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 }$ TTwo samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \underset { 1 } { 2 } \neq \sigma _ { 2 } ^{ 2 }$ At a
Level of significance of α $\alpha$ = 0.20, when should you reject H₀? $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } }_ 1 = 2.9 & \overline { \mathrm { x } }_ 2 = 3.3 \
\mathrm {~s} _1 = 0.76 & \mathrm {~s}_ 2 = 0.51
\end{array}$$
A)Reject H₀ if the standardized test statistic is less than -1.372 or greater than 1.372.
B)Reject H₀ if the standardized test statistic is less than -0.684 or greater than 0.684.
C)Reject H₀ if the standardized test statistic is less than -2.228 or greater than 2.228.
D)Reject H₀ if the standardized test statistic is less than -3.169 or greater than 3.169.

Question

Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 }$ TTwo samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \underset { 1 } { 2 } \neq \sigma _ { 2 } ^{ 2 }$ At a
Level of significance of α $\alpha$ = 0.20, when should you reject H₀? $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } }_ 1 = 2.9 & \overline { \mathrm { x } }_ 2 = 3.3 \
\mathrm {~s} _1 = 0.76 & \mathrm {~s}_ 2 = 0.51
\end{array}$$
A)Reject H₀ if the standardized test statistic is less than -1.372 or greater than 1.372.
B)Reject H₀ if the standardized test statistic is less than -0.684 or greater than 0.684.
C)Reject H₀ if the standardized test statistic is less than -2.228 or greater than 2.228.
D)Reject H₀ if the standardized test statistic is less than -3.169 or greater than 3.169.

Quizplus · Accepted Answer

Given the unequal variances ($\sigma_1^2 \neq \sigma_2^2$), and the sample sizes, we use the Welch's t-test approach for hypothesis testing about means. The critical t-value for a two-tailed test with $\alpha = 0.20$ (or a significance level of 20%) will be less extreme than for more common levels like 0.05 or 0.01, hence option A's range is the most plausible for this level of $\alpha$, considering the degrees of freedom would be adjusted and not simply n-1 due to the Welch-Satterthwaite equation.

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

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