Question

A study of a sample of 110 supermarkets reveals that 31 offer carrier bags suitable to
shoppers. Construct a 95% interval estimate of the proportion of all supermarkets that
have these carrier bags

i. How many supermarkets would have to be included in the sample if the
confidence interval of the proportion of establishments with carrier bags has
to be within 5% of the actual population proportion with a 95% level of
confidence. [4 marks

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 31 / 110 = 0.282

1 - = 1 - 0.282 = 0.718

margin of error = E = 0.05

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 / 0.05)2 * 0.282 * 0.718

= 311.13

sample size = n = 312