SCENARIO 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 and 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 Scenario 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

SCENARIO 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  and  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 Scenario 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.

Quizplus · Accepted Answer

We need to conduct a two-sample z-test for the difference in proportions with the following hypotheses:

Null hypothesis: p1 - p2 = 0 (The proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 Years.)
Alternative hypothesis: p1 - p2 ≠ 0 (The proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years.)

where p1 represents the proportion of employees interested in the recent study and p2 represents the proportion of employees interested in the past study.

Using a significance level of 0.05, we find the critical value using a standard normal distribution:

z = ±1.96

The test statistic is calculated as:

z = (p1 - p2) / sqrt(p_bar*(1-p_bar)*[1/n1 + 1/n2])

where p_bar = (x1 + x2) / (n1 + n2) = (0.66*150 + 0.6*160) / (150 + 160) = 0.63, x1 = 0.66*150 = 99, x2 = 0.6*160 = 96, n1 = 150, and n2 = 160.

Plugging in the values gives:

z = (0.66 - 0.6) / sqrt(0.63*(1-0.63)*[1/150 + 1/160]) = 1.05

Since 1.05 < 1.96, 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.

SCENARIO 10-10 a Corporation Randomly Selects 150 Salespeople and Finds