Question

Consider random samples of size 50 from a population with proportion 0.15

Find the mean and standard error of the distribution of sample proportions.

Round your answer for the mean to two decimal places, and your answer for the standard error to three decimal places.

mean =

Standard error =

Is the sample size large enough for the Central Limit Theorem to apply? yes or no

Answer 1

Answer:

a) Mean = 0.75

b) Standard error = 0.051

c) Yes                              

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 50

Sample proportion , p = 0.15

a) Mean

$\mu = np = 50(0.15) = 7.5$

b) Standard error

$S.E = \sqrt{\dfrac{p(1-p)}{n}} = \sqrt{\dfrac{0.15(1-0.15)}{50}} = 0.051$

c) Application of central limit theorem

Since the sample size is larger than 30, we cam apply central limit theorem for normal approximation.