TABLE 12-5
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let u₁and u₂represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Table 12-5, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

Question

TABLE 12-5
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let u 1   and u 2   represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Table 12-5, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?
A) $ H_{0}: \pi_{1}-\pi_{2}=0 $ versus $ H_{1}: \pi_{1}-\pi_{2} \neq 0 $
B) $ H_{0}: \pi_{1}-\pi_{2} \leq 0 $ versus $ H_{1}: \pi_{1}-\pi_{2}>0 $
C) $ H_{0}: \pi_{1}-\pi_{2} \geq 0 $ versus $ H_{1}: \pi_{1}-\pi_{2}<0 $
D) $ H_{0}: \pi_{1}-\pi_{2} \neq 0 $ versus $ H_{1}: \pi_{1}-\pi_{2}=0 $

Quizplus · Accepted Answer

The hypothesis test is to determine if there is a change in the proportion of salespeople who would like to attend a self-improvement course between the two studies. Therefore, the null hypothesis $ H_{0} $ is that there is no difference in proportions ($ \pi_{1}-\pi_{2}=0 $), and the alternative hypothesis $ H_{1} $ is that there is a difference ($ \pi_{1}-\pi_{2} \neq 0 $).

TABLE 12-5 a Corporation Randomly Selects 150 Salespeople and Finds H0:π1−π2=0 H_{0}: \pi_{1}-\pi_{2}=0 H0​:π1​−π2​=0

TABLE 12-5
a Corporation Randomly Selects 150 Salespeople and Finds $H_{0}: \pi_{1}-\pi_{2}=0$