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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

Math   Statistics-And-Probability   
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Answer #1

This a hypothesis test for population proportion.

We use a normal approximation for it.

Margin of error = Critical value * Standard error

Critical value =

Where = 1 - 0.99 = 0.01

Critical value =

= 2.5758 ..................using normal distribution percentage tables

Standard error =

Where sample proportion = 0.65

Standard error =

We have been given MOE = 2%

We solve for 'n' by taking square on both sides

The change in the value might be due to rounding off.

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