Lemons tastes sour to some people. This sourness is inherited through the TAS2R38 gene. About 65%...

Lemons tastes sour to some people. This sourness is inherited through the TAS2R38 gene. About 65% 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 2% margin of error and 99% confidence, to estimate the proportion of people who carry the TAS2R388 gene?

A. 569 people

B. 1,138 people

C. 5 people

D. 78 people

E. 3775 people

Expert Solution

p=65% =0.65

q=1-p =1-0.65

=0.35

For 99% confidence,Zα/2 =2.576

E=2% =0.02

Margin of error,E =Zα/2 × √[(p×q)/n]

0.02 = 2.576 x√(0.65*0.35)/√n

0.02 =2.576x0.47696/√n

0.02 =1.22867/√n

√n =1.22867/0.02

√n =61.43368

n=(61.43368)^2

n=3775

so its choice E,3775 people

orchestra answered 2 years ago

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