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 $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ Use $\alpha$ = 0.05. $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \
\overline { \mathrm { x } } 1 = 15 & \overline { \mathrm { x } } 2 = 16 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) $\pm 2.064$
B) $\pm 2.492$
C) $\pm 1.711$
D) $\pm 1.318$

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 $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ Use $\alpha$ = 0.05. $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \
\overline { \mathrm { x } } 1 = 15 & \overline { \mathrm { x } } 2 = 16 \
\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) $\pm 2.064$
B) $\pm 2.492$
C) $\pm 1.711$
D) $\pm 1.318$

Quizplus · Accepted Answer

Since the population variances are assumed to be equal ($\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$), we use the pooled variance method to find the degrees of freedom. The degrees of freedom (df) is $n_1 + n_2 - 2 = 14 + 12 - 2 = 24$. For a two-tailed test with $\alpha = 0.05$, we look up the critical value for 24 degrees of freedom in the t-distribution table, which gives us $\pm 2.064$.

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

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