Find the critical value, $t _ { 0 }$ 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 $\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 }^ { 2 }$ Use α = 0.01. $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 600 & \overline { \mathrm { x } _ { 2 } } = 585 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A)2.681
B)1.699
C)2.179
D)3.055

Question

Find the critical value, $t _ { 0 }$ 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 $\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 }^ { 2 }$ Use α = 0.01. $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \
\overline { \mathrm { x } } 1 = 600 & \overline { \mathrm { x } _ { 2 } } = 585 \
\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25
\end{array}$$
A)2.681
B)1.699
C)2.179
D)3.055

Quizplus · Accepted Answer

Given the unequal variances ($\sigma_1^2 \neq \sigma_2^2$), we use the Welch's t-test formula to find the degrees of freedom (df) for the critical value. The formula for df in this context is complex, but it approximates the degrees of freedom for a t-distribution when the sample variances and sizes are unequal. After calculating df, we look up the critical value for a one-tailed test with $\alpha = 0.01$. The closest match among the provided options is 2.681, which corresponds to a high confidence level (99%) for rejecting the null hypothesis if the t-statistic is beyond this critical value.

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

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