In a large high school, 37 percent of the teachers believe that five minutes is not enough time for students to change classes. However, 89 percent of the students believe that five minutes is not enough time for students to change classes. Let hat p sub cap f and hat p sub cap s be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the mean of the sampling distribution of hat p sub cap f minus hat p sub cap s ?
The mean of the sampling distribution of the difference in sample proportions is the difference between the population proportions: 0.37 − 0.89 = −0.52. Therefore, the mean is negative 0.52, which is choice C.
AI-written and checked against the verified answer.