Question

Suppose that 79% of students wear glasses. A survey is taken of 100 students and 78 of those wear glasses.

What is the mean of the sampling distribution for the sample proportion, p-hat?

What is the standard error of the sampling distribution for the sample proportion

	A.	0.0079
	B.	0.0021
	C.	0.7900
	D.	0.2100

Answer 1

Solution

Back-up Theory

If p_hat is the sample proportion and p is the population proportion, then,

mean of the sampling distribution for the sample proportion, p-hat = p ……....................…. (1)

standard error of the sampling distribution for the sample proportion = √{p(1 - p)/n} ............ (2)

Now to work out the solution,

We have n = 100, p = 0.79 [i.e., 79%], p_hat = 78/100 = 0.78.

So, vide (1), Option C Answer 1

Vide (2),

standard error of the sampling distribution for the sample proportion

= √{(0.79 x 0.21)/100}

= 0.0407 Answer 2

DONE