Question

at a large University the graduation rate for the general student body was reported to be 0.66 we want to compare the center spread and shape of the distribution of sample proportion graduating from random samples of five students compared to the distribution and random samples of 50 students what is the center of the distribution for samples of size 5 round the answer to two decimal places

Answer 1

Given p = 0.66 and n = 5

Center: The mean of the sample proportion phat should be equal to population proportion p = 0.66

Spread: For a sample of Size n = 5,

         sqread = sqrt(npq) = sqrt(5*0.66*0.34) =1.059

Shape: For a sample of size n = 5, as per approximate normality of sample proporiton,

           np = 5*0.66 = 3.3 which is less than 10 and np = 5*0.34= 1.7 which is less than 10.

So, the shape of the distribution phat is not normal

Given p = 0.66 and n = 50

Center: The mean of the sample proportion phat should be equal to population proportion p = 0.66

Spread: For a sample of Size n = 50,

         sqread = sqrt(npq) = sqrt(50*0.66*0.34) =3.3496

Shape: For a sample of size n = 50, as per approximate normality of sample proporiton,

           np = 50*0.66 = 33 which is greater than 10 and np = 50*0.34= 17 which is also greater than 10.

So, the shape of the distribution phat is t normal