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 10-10, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is correct?
A) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years.
B) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years.
C) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.
D) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.

Question

Quizplus · Accepted Answer

To test whether there is a significant change in the proportion of employees who are interested in a self-improvement course over the 10-year period, we can use a two-sample z-test for proportions. 
The null hypothesis is that there is no difference between the proportions in the two samples, i.e. H0: π₁ = π₂. 
The alternative hypothesis is that the proportions are different, i.e. Ha: π₁ ≠ π₂. 
Using the formulas for the standard error of the difference between two proportions, we obtain a test statistic of -1.17 and a p-value of 0.243. 
Since the p-value is greater than the 0.05 significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years. Therefore, the correct answer is B, do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years.

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