Find the critical values, $\mathrm { t } _ { 0 } ,$ to test the claim that $\mu _ { 1 } = \mu 2$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } \text {. }$ Use $\alpha$ = 0.05. $$\begin{array} { l }
\mathrm { n } _ { 1 } = 25 \
\overline { \mathrm { x } } 1 = 17 \
\mathrm {~s} _ { 1 } = 1.5
\end{array}$$ $$\begin{array} { l }
\mathrm { n } _ { 2 } = 30 \
\overline { \mathrm { x } _ { 2 } } = 15 \
\mathrm {~s} _ { 2 } = 1.9
\end{array}$$
A) $\pm 2.064$
B) $\pm 2.797$
C) $\pm 1.711$
D)± $\pm 2.492$

Question

Find the critical values, $\mathrm { t } _ { 0 } ,$ to test the claim that $\mu _ { 1 } = \mu 2$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } \text {. }$ Use $\alpha$ = 0.05. $$\begin{array} { l } 
\mathrm { n } _ { 1 } = 25 \
\overline { \mathrm { x } } 1 = 17 \
\mathrm {~s} _ { 1 } = 1.5
\end{array}$$ $$\begin{array} { l } 
\mathrm { n } _ { 2 } = 30 \
\overline { \mathrm { x } _ { 2 } } = 15 \
\mathrm {~s} _ { 2 } = 1.9
\end{array}$$
A) $\pm 2.064$
B) $\pm 2.797$
C) $\pm 1.711$
D)± $\pm 2.492$

Quizplus · Accepted Answer

The correct critical values for a two-sample t-test with unequal variances (assuming normal distributions and independent samples) at a significance level of $\alpha = 0.05$ and with degrees of freedom calculated using the Welch-Satterthwaite equation are $\pm 2.064$. This value corresponds to the t-distribution critical values for a two-tailed test at this significance level, given the degrees of freedom are not specified but typically fall into a range where this value is applicable for a 0.05 alpha level.

Find the Critical Values t0,\mathrm { t } _ { 0 } ,t0​,

Find the Critical Values $\mathrm { t } _ { 0 } ,$