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

Answer:

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:

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

Where:

$z_{\frac{0.01}{2}}=2.576$ is the critical value at 0.01 significance level.

Therefore, the required sample size is:

$n=0.65(1-0.65) \left(\frac{2.576}{0.02} \right)^{2}$

      $=0.2275 \times 16589.44$

      $=3774.1 \approx 3774$

Therefore, the required sample size is 3774