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

The standard deviation is equal to sqrt(n*p*(1-p))

For teachers the SDt would be sqrt(28 * 0.37 * 0.63) = 2.55

For students the SDs would be sqrt(100*0.89 * 0.11) = 3.12

The calculation of the SD of the sampling proportion distribution of pt(hat) - ps(hat0 = sqrt(SDt^2 + SDs^2) = sqrt(2.55^2 + 3.12^2) = 4.03