Question

Impact of Sample Size on Accuracy Compute the standard error for sample proportions from a population with proportion p = 0.35 for sample sizes of n = 20, n = 250, and n = 1100.

Answer 1

Solution:

Given that,

a ) n = 20

P = 0.35

1 - P = 1 - 0.35 = 0.65

_P = P ( 1 - P ) / n

_P =  (0.35 * 0.65 ) / 20

= 0.1066

_P = 0.1066

Standard error = 0.1066

b ) n = 250

P = 0.35

1 - P = 1 - 0.35 = 0.65

_P = P ( 1 - P ) / n

_P =   (0.35 * 0.65 ) / 250

= 0.0302

_P = 0.0302

Standard error = 0.0302

c ) n = 1100

P = 0.35

1 - P = 1 - 0.35 = 0.65

_P = P ( 1 - P ) / n

_P =  (0.35 * 0.65 ) / 1100

= 0.0144

_P = 0.0144

Standard error = 0.0144