Question on Sample Proportion

Question

In a large high school, 37% of the teachers believe that five minutes is not enough to time for students to change classes. However, 89% of students believe that five minutes is not enough time for students to change classes. Let p_t (hat) and p_s (hat) 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 students teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change classes

What is the correct calculation and interpretation of the standard deviation of the sampling proportion distribution of p_t (hat) –  p_s (hat)?

Answer 1

=sqrt((0.37*(1-0.37)/28)+(0.89*(1-0.89)/100)) = 0.0965

The difference in sample proportions (teachers - students) that believe 5 minutes is not enough time between classes typically varies by about 0.0965 from the true difference in proportions.