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,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)4.335
B)1.96
C)1.093
D)0

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,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)4.335
B)1.96
C)1.093
D)0

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, calculated as $$p = \frac{x_1 + x_2}{n_1 + n_2}$$ with $x_1$ and $x_2$ being the number of successes in each sample. Given $\hat{p}_1 = 0.66$, $\hat{p}_2 = 0.60$, $n_1 = 150$, and $n_2 = 160$, we find $p = \frac{(0.66*150) + (0.60*160)}{150 + 160}$ and then plug these values into the formula for $Z$. The calculation yields a value close to 1.093, indicating that the correct choice is C.

SCENARIO 10-10 a Corporation Randomly Selects 150 Salespeople and Finds π\piπ

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