Question

In a random sample of 100 manufacturing firms, 65 indicated that their company attained ISO certification within the last two years. Suppose we have large sample, use the sampling distribution of sample proportion ?̂ and construct a 90% confidence interval for the population proportion of companies that have been certified within the last two years. Interpret the result.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 65 / 100 = 0.65

1 - = 1 - 0.65 = 0.35

Z/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 (((0.65 * 0.35) / 100)

= 0.078

A 90% confidence interval for population proportion p is ,

± E   

= 0.65  ± 0.078

= ( 0.572, 0.728 )

We are 90% confident that the population proportion of companies that have been certified within the last two years between 0.572 and 0.728.