Question

Broccoli tastes bitter to some people. This bitterness is inherited through the TAS2R38 gene. About 52% of the population has this gene. You want to estimate the proportion of Americans who have this gene. How large a sample must you test, with a 5% margin of error and 90% confidence, to estimate the proportion of people who carry the TAS2R38 gene?

100 people
10,000 people
271 people
37 people
514 people

Answer 1

271 people

Explanation:

Margin of error = critical value × standard error

At 90% confidence, the critical value is 1.645.

Standard error for a proportion is s = √(p (1 − p) / n).

0.05 = 1.645 √(0.52 (1 − 0.52) / n)

n = 271