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.

Answer 1

Confidence interval for Population Proportion is given as below:

Confidence Interval = p̂ ± Z* sqrt(p̂*(1 – p̂)/n)

Where, p̂ is the sample proportion, Z is critical value, and n is sample size.

We are given

Number of items of interest = x = 408

Sample size = n = 2322

Sample proportion = p̂ = x/n = 408/2322 = 0.175710594

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Confidence Interval = p̂ ± Z* sqrt(p̂*(1 – p̂)/n)

Confidence Interval = 0.175710594 ± 1.6449* sqrt(0.175710594*(1 – 0.175710594)/ 2322)

Confidence Interval = 0.175710594 ± 1.6449*0.0079

Confidence Interval = 0.175710594 ± 0.012991

Lower limit = 0.175710594 - 0.012991 = 0.163

Upper limit = 0.175710594 + 0.012991 = 0.189

Confidence interval = (0.163, 0.189)