Question

Admissions records at a small university indicate that 6.7% of the students enrolled are international students. Find the mean and standard error of the sample proportion of international students in random samples of size 50. Use four decimal places when reporting the standard error.

Answer 1

The mean of the sample proportion of international students is 0.067, and the standard error for a sample size of 50 is 0.0353.

Step-by-step explanation:

To find the mean of the sample proportion of international students in random samples of size 50 at a small university where 6.7% of the students enrolled are international students, we would use the population proportion, p, which is given as 6.7% or 0.067. The mean of the sample proportion (π') is the same as the population proportion, so π' = 0.067.

The standard error (SE) of the sample proportion is calculated using the formula SE = √p(1-p)/n, where p is the population proportion and n is the sample size. Using the given data, SE = √(0.067)(1-0.067)/50 = √0.062411/50 = √0.00124822 = 0.0353 (rounded to four decimal places).

Therefore, the mean of the sample proportion is 0.067 and the standard error is 0.0353.