Question

a survey of 2280 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 409 have donated blood in the past two years.

construct and interpret a 90% confidence interval for the population proportion of adults in the country who have donated blood in the past two years.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 409 / 2280 = 0.179

1 - = 1 - 0.179 = 0.821

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.179 * 0.821) / 2280)

= 0.013

A 90% confidence interval for population proportion p is ,

± E

= 0.179 ± 0.013

= ( 0.166, 0.192 )

We are 90% confident that the true proportion of adults in the country who have donated blood in the past two years between 0.166 and 0.192.