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,what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions?
A) 0
B) 1.96
C) 1.093
D) 4.335

Question

Quizplus · Accepted Answer

The test statistic for the difference between two proportions is calculated using the formula: $z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}}$, where $\hat{p}_1$ and $\hat{p}_2$ are the sample proportions, $n_1$ and $n_2$ are the sample sizes, and $p$ is the pooled proportion. Given $\hat{p}_1 = 0.66$, $\hat{p}_2 = 0.60$, $n_1 = 150$, $n_2 = 160$, and $p = \frac{0.66*150 + 0.60*160}{150+160}$, the calculation yields a z-value close to 1.093, indicating the test statistic to evaluate the difference in proportions.

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