Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.02$ $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } } 1 = 3.9 & \overline { \mathrm { x } _ { 2 } } = 4.3 \
\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$
A) $\pm 2.764$
B) $\pm 0.684$
C) $\pm 2.228$
D) $\pm 3.169$

Question

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.02$ $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } } 1 = 3.9 & \overline { \mathrm { x } _ { 2 } } = 4.3 \
\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$
A) $\pm 2.764$
B) $\pm 0.684$
C) $\pm 2.228$
D) $\pm 3.169$

Quizplus · Accepted Answer

The critical value for a two-tailed test with unequal variances (assuming normal distributions for both populations) and a significance level of $\alpha = 0.02$ can be found using the t-distribution. Since the variances are unequal and the sample sizes are different, we use the Welch-Satterthwaite equation to approximate the degrees of freedom. However, the exact degrees of freedom calculation is not provided here, but given the options and the significance level, $\pm 2.764$ corresponds to a critical value that might be used for a two-tailed test with a low degree of freedom and a significance level close to $\alpha = 0.02$, making it the most plausible choice among the given options.

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

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