Find the critical valuevalue, $t _ { 0 }$ to test the claim that $\mu _ { 1 }

Question

Find the critical valuevalue, $t _ { 0 }$ 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 $$\sigma { } _ { 1 } ^ { 2 } = \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.05$$ $$\begin{array} { l } 
\mathrm { n } _ { 1 } = 15 \
\overline { \mathrm { x } } _ { 1 } = 22.2 \
\mathrm {~s} _ { 1 } = 2.9
\end{array}$$ $$\begin{array} { l } 
\mathrm { n } _ { 2 } = 15 \
\overline { \mathrm { x } _ { 2 } } = 24.75 \
\mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A)-1.701
B)2.467
C)-1.313
D)0.683

Quizplus · Accepted Answer

Given that the two samples are independent, from populations that are normally distributed, and assuming equal variances ($\sigma_1^2 = \sigma_2^2$), we use the t-distribution to find the critical value for a one-tailed test (since the claim is $\mu_1 < \mu_2$) with $\alpha = 0.05$. The degrees of freedom (df) for two samples where $n_1 = n_2 = 15$ and assuming equal variances can be calculated as $df = n_1 + n_2 - 2 = 15 + 15 - 2 = 28$. Looking up the critical value for a one-tailed test with $\alpha = 0.05$ and $df = 28$ gives us a critical value close to -1.701, which corresponds to choice A.

Find the Critical Valuevalue t0t _ { 0 }t0​ To Test the Claim That

Find the Critical Valuevalue $t _ { 0 }$ To Test the Claim That