Question

A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years. Round your answer to three decimal places.

a. (0.163, 0.189)

b. (0.160, 0.191)

c. (0.156, 0.196)

d. (0.154, 0.198)

Answer 1

The 90% confidence interval for the Population Proportion of adults in US who have donated blood in the past two years (P) is given by -

where, p is the sample proportion = 408/2322 = 0.176

n is the sample size = 2322

is the critical value of z for two tailed test at 0.10 level of significance = 1.65

(It can be obtained from the z table by finding the z for which area is nearly equal to 0.10 which will be at 1.65 i.e z = 1.6 at 0.05 probability)

So, the confidence interval will be -

= [ 0.163, 0.189]

Hence, Option (a) will be the correct option.

We are 90% confident that the true population proportion of US adults who have voted in the past two years will lie between 0.163 and 0.189