TABLE 10-10
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 10-11, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

Question

TABLE 10-10
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 10-11, 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 proportions are equal)
H₁: π₁ - π₂ ≠ 0 (the proportions are not equal)
This is a two-tailed test because we are interested in whether the population proportion has either increased or decreased from the previous study. Therefore, choice A is the best option. Choice B is incorrect because it represents a one-tailed test, which is not appropriate in this situation. Choices C and D are incorrect because they do not allow for the possibility of the proportions being equal, which is included in the null hypothesis.

TABLE 10-10 A Corporation Randomly Selects 150 Salespeople and Finds That 66