Question

A survey of 2322 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 418 have donated blood in the past two years. Complete parts​ (a) through​ (c) below.

a) Obtain a point estimate for the population proportion of adults in the country aged 18 and older who have donated blood in the past two years.

​(b) Verify that the requirements for constructing a confidence interval about p are satisfied.

​(c) 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. Select the correct choice below and fill in any answer boxes within your choice.

Answer 1

a) Point estimate of the population proportion is the sample proportion , given by

b) n = 2322 is large

np = 2322*0.18 = 418 > 10

n(1-p) = 2322*(1-0.18) = 1904> 10

Thus requirements for constructing confidence interval are satisfied .

c) The 90% confidence interval for p is

For 90% confidence , zc = 1.65

Thus , 90% confidence interval is

= (0.1668 , 0.1932) ( up to four decimal )

= (0.17 ,0.19 ) (up to 2 decimal)

Interpretation

We are 90% confident that the true population proportion adults in the country who have donated blood in the past two years lies between 0.17 and 0.19 .