A paired difference experiment yielded $\mathrm { n } _ { \mathrm { d } }$ pairs of observations. For the given case, what is the rejection region for testing $\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 15$ against Ha: $\mu _ { \mathrm { d } } < 15$ ?
$\mathrm { n } _ { \mathrm { d } } = 19 , \alpha = 0.01$

Question

A paired difference experiment yielded $\mathrm { n } _ { \mathrm { d } }$ pairs of observations. For the given case, what is the rejection region for testing $\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 15$ against Ha: $\mu _ { \mathrm { d } } < 15$ ?
$$\mathrm { n } _ { \mathrm { d } } = 19 , \alpha = 0.01$$
A) $t < 2.552$
B) $t < - 2.552$
C) $t < 2.861$
D) $t < - 2.539$

Quizplus · Accepted Answer

The rejection region for a left-tailed test (since Ha: $\mu_d < 15$) at $\alpha = 0.01$ with $n_d = 19$ (degrees of freedom = 18) is determined by looking up the critical value in a t-distribution table for $\alpha = 0.01$ and 18 degrees of freedom. The negative sign indicates the direction of the tail for the test (left-tailed), and the value closest to this description is $-2.552$, making option B correct.

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

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