Find the critical value, $t _ { 0 } ,$ to test the claim that $\mu _ { \mathrm { d } }$ = 0. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha$ = 0.01. $$\begin{array} { r | r r r r r }
\text { A } & 8.2 & 9.2 & 11.1 & 8.1 & 8.2 \
\hline \text { B } & 10.6 & 9.5 & 9.4 & 9.3 & 10.7
\end{array}$$
A) $\pm 4.604$
B) $\pm 3.747$
C)2.132
D)0.741

Question

Find the critical value, $t _ { 0 } ,$ to test the claim that $\mu _ { \mathrm { d } }$ = 0. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha$ = 0.01. $$\begin{array} { r | r r r r r } 
\text { A } & 8.2 & 9.2 & 11.1 & 8.1 & 8.2 \
\hline \text { B } & 10.6 & 9.5 & 9.4 & 9.3 & 10.7
\end{array}$$
A) $\pm 4.604$
B) $\pm 3.747$
C)2.132
D)0.741

Quizplus · Accepted Answer

The critical value for a two-tailed test with $\alpha = 0.01$ and degrees of freedom (df) less than 30 (since sample size is small and df = n - 1 for dependent samples, where n is the number of pairs) typically requires looking up a t-table or using statistical software. For very small sample sizes and a high confidence level (99% in this case, given $\alpha = 0.01$), the critical value tends to be high. Among the provided options, $\pm 4.604$ is the only one that matches the expectation for a high critical value in a scenario with a small sample size and a stringent significance level.

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

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