SCENARIO 12-1
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 12-1,what is the critical value when performing a chi-square test on whether the population proportions are different if ? = 0.05?
A)$\pm$1.645
B)$\pm$1.96
C)3.841
D)2.706

Question

SCENARIO 12-1
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 12-1,what is the critical value when performing a chi-square test on whether the population proportions are different if ? = 0.05?
A)$\pm$1.645
B)$\pm$1.96
C)3.841
D)2.706

Quizplus · Accepted Answer

Since we are performing a chi-square test for independence, we need to find the critical value from the chi-square distribution with (r-1)(c-1) degrees of freedom, where r and c are the number of rows and columns in our contingency table. In this case, we have two proportions being compared, so we have a 2x2 contingency table with one degree of freedom. Using a chi-square distribution table or calculator with α = 0.05 and one degree of freedom, we find the critical value to be 3.841. Therefore, choice C is the correct answer.

SCENARIO 12-1 a Corporation Randomly Selects 150 Salespeople and Finds π\piπ

SCENARIO 12-1
a Corporation Randomly Selects 150 Salespeople and Finds $\pi$