TABLE 12-1
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 π₁ and π₂ 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 12-1, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

Question

TABLE 12-1
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 π₁ and π₂ 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 12-1, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?
A) H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0
B) H₀: π₁ - π₂ ≠ 0 versus H₁: π₁ - π₂ = 0
C) H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0
D) H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0

Quizplus · Accepted Answer

The relevant hypotheses for testing whether the proportion has changed from the previous study are:
H₀: π₁ - π₂ = 0 (the proportion of workers who want to attend the self-improvement course has not changed)
H₁: π₁ - π₂ ≠ 0 (the proportion of workers who want to attend the self-improvement course has changed, either increased or decreased). 
This is a two-tailed test, as we are testing whether the proportion has changed in either direction. Therefore, the correct choice is A.

TABLE 12-1 A Corporation Randomly Selects 150 Salespeople and Finds That 66