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 $\pi$ 1 and $\pi$ 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 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  $\pi$ 1 and  $\pi$ 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 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 are testing for a change in proportion, therefore our null hypothesis is:
H0: F1=S1
Our alternative hypothesis is:
Ha: F1≠S1
We will use a two-sample z-test since the two groups are assumed to be independent random samples. The test statistic is:
z=(̂F1−̂S1)−0/(√((̂F1(1−̂F1))/n1)+((̂S1(1−̂S1))/n2))=1.16
Using a two-tailed test with α=0.05 and a z-table, the critical values are ±1.96. Since the calculated z-value of 1.16 is between these critical values, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude 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 π\piπ

SCENARIO 10-10
a Corporation Randomly Selects 150 Salespeople and Finds $\pi$