A paired difference experiment yielded $\mathrm { n } _ { \mathrm { d } }$ pairs of observations. For the given case, what is the rejection region for testing $\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 9$ against Ha: $\mu _ { \mathrm { d } } \neq 9$ ?
$$\mathrm { n } _ { \mathrm { d } } = 13 , \alpha = 0.05$$
A) $t 1.782$
B) $t 2.179$
C) $| t | 2.160$
D) $| t | 2.179$

Question

A paired difference experiment yielded $\mathrm { n } _ { \mathrm { d } }$ pairs of observations. For the given case, what is the rejection region for testing $\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 9$ against Ha: $\mu _ { \mathrm { d } } \neq 9$ ?
$$\mathrm { n } _ { \mathrm { d } } = 13 , \alpha = 0.05$$
A) $t > 1.782$
B) $t > 2.179$
C) $| t | > 2.160$
D) $| t | > 2.179$

Quizplus · Accepted Answer

For a two-tailed test with $\alpha = 0.05$ and $n_d = 13$ (degrees of freedom $n_d - 1 = 12$), the critical t-value from a t-distribution table for a 95% confidence level (or 5% significance level split across two tails) is approximately 2.179. Therefore, the rejection region for testing $\mu_d \neq 9$ is where the absolute value of the test statistic $|t|$ is greater than 2.179.

A Paired Difference Experiment Yielded nd\mathrm { n } _ { \mathrm { d } }nd​

A Paired Difference Experiment Yielded $\mathrm { n } _ { \mathrm { d } }$