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

Question

Angelina Reed

Mathematics

13 April, 10:37

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

+3

Answers (1)

Know the Answer?

Gwendolyn · Answer 1

271 people

Step-by-step 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