Question

A random sample of 125 students is taken from the population of all part-time students in the United States, for which the overall proportion of females is 0.6. Identify the mean of the sampling distribution for the proportion of female part-time students.

a) 0.48

b) 0.6

c) 0.52

d) 0.64

Answer 1

To find the mean of the sampling distribution for the proportion of female part-time students, we use the formula for standard error of the proportion. Hence the correct answer is option B

Step-by-step explanation:

To identify the mean of the sampling distribution for the proportion of female part-time students, we need to use the formula for the standard error of the proportion:

Standard Error = sqrt((p*q)/n)

Where p is the proportion of females in the population, q is 1-p, and n is the sample size.

In this case, p = 0.6, q = 0.4, and n = 125. Plugging these values into the formula, we get:

Standard Error = sqrt((0.6 * 0.4) / 125) = sqrt(0.24 / 125) = sqrt(0.00192) = 0.0438

The mean of the sampling distribution is equal to the proportion of females in the population, so the answer is b) 0.6.