Question

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?

Answer 1

3775

Explanation:

I took the test

Answer 2

We are given:

`\hat{p}=0.65`

Margin of error
`E=0.02`

Confidence level = 0.99

We need to find the sample size to estimate the proportion of people who carry the TAS2R388 gene.

The formula for finding the sample size is:

`n=\hat{p} (1-\hat{p})\left (\frac{z_{(0.01)/(2)}}{E} \right )^(2)`

Where:

`z_{(0.01)/(2)}=2.576` is the critical value at 0.01 significance level.

Therefore, the required sample size is:

`n=0.65(1-0.65) \left((2.576)/(0.02) \right)^(2)`

`=0.2275 * 16589.44`

`=3774.1 \approx 3774`

Therefore, the required sample size is 3774