Instruction 10-12
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 π 1 and π 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 Instruction 10-12,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 most 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) 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.
C) 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.
D) 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.

Question

Quizplus · Accepted Answer

We can set up the hypotheses as follows:

H0: π1 = π2 (the proportion has not changed from the previous study)
Ha: π1 ≠ π2 (the proportion has changed from the previous study)

We want to test at the 0.05 level, which means we need to find the critical value(s) for a two-tailed test. Using a significance level of 0.05, we have:

α/2 = 0.025
df = n1 + n2 - 2 = 150 + 160 - 2 = 308
t* = ±1.965

Now we can calculate the test statistic:

t = (p1 - p2) / sqrt(pooled * (1 - pooled) * (1/n1 + 1/n2))
where pooled = (x1 + x2) / (n1 + n2) = (0.66*150 + 0.60*160) / (150 + 160) = 0.63
and x1 = 0.66*150 = 99, x2 = 0.60*160 = 96

t = (0.66 - 0.60) / sqrt(0.63 * 0.37 * (1/150 + 1/160)) = 1.34

Since |t| < t*, we fail to reject the null hypothesis. Therefore, we can 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. The correct choice is D.

Instruction 10-12 A Corporation Randomly Selects 150 Salespeople and Finds That 66