Question

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

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.