Use the following information for questions:
In a random sample of 250 full time students, 80% preferred to have three one-hour lectures per week rather than two 90-minute lectures. In a random sample of 500 part-time students, 50% said they preferred the three one-hour lectures schedule. The difference between the two sample proportions (full-time - part-time) is to be calculated.
-Which of the following choices correctly denotes the difference between the two sample proportions that is to be calculated?
A) $ p_1 $ - $ p_2 $ = 0.30
B) $ p_1 $ - $ p_2 $ = -0.30
C) $ \hat{p_1} $ - $ \hat{p_2} $ = 0.30
D) $ \hat{p_1} $ - $ \hat{p_2} $ = -0.30

Question

Use the following information for questions:
 In a random sample of 250 full time students, 80% preferred to have three one-hour lectures per week rather than two 90-minute lectures. In a random sample of 500 part-time students, 50% said they preferred the three one-hour lectures schedule. The difference between the two sample proportions (full-time - part-time) is to be calculated.
-Which of the following choices correctly denotes the difference between the two sample proportions that is to be calculated?
A) $ p_1 $ - $ p_2 $ = 0.30
B) $ p_1 $ - $ p_2 $ = -0.30
C) $ \hat{p_1} $ - $ \hat{p_2} $ = 0.30
D) $ \hat{p_1} $ - $ \hat{p_2} $ = -0.30

Quizplus · Accepted Answer

The difference between the two sample proportions ($ \hat{p_1} $ - $ \hat{p_2} $) is calculated using the sample proportions, not the population proportions. Here, 80% (or 0.80) of full-time students and 50% (or 0.50) of part-time students preferred the three one-hour lectures, making the difference 0.80 - 0.50 = 0.30.

Use the Following Information for Questions: in a Random p1 p_1 p1​

Use the Following Information for Questions:
in a Random $p_1$