Question

Consider a population proportion p = 0.68. Calculate the expected value and the standard error of with n = 20. Is it appropriate to use the normal distribution approximation for ? Calculate the expected value and the standard error of with n = 50. Is it appropriate to use the normal distribution approximation for ?

Answer 1

Answer: a) 0.68, 0.1043, b) 0.68, 0.066

Step-by-step explanation:

Since we have given that

p = 0.68

n= 20

Expected value = 0.68

So, Standard error would be

$\sqrt{\dfrac{p(1-p)}{n}}\\\\=\sqrt{\dfrac{0.68\times 0.32}{20}}\\\\=0.1043$

if n = 50

Expected value = 0.68

So, Standard error would be

$\sqrt{\dfrac{p(1-p)}{n}}\\\\=\sqrt{\dfrac{0.68\times 0.32}{50}}\\\\=0.0659\approx 0.066$

In both the cases,

Yes it is appropriate to use the normal distribution for expected value and standard error.