Respuesta :
Answer:
We are given:
[tex]\hat{p}=0.65[/tex]
Margin of error [tex]E=0.02[/tex]
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:
[tex]n=\hat{p} (1-\hat{p})\left (\frac{z_{\frac{0.01}{2}}}{E} \right )^{2}[/tex]
Where:
[tex]z_{\frac{0.01}{2}}=2.576[/tex] is the critical value at 0.01 significance level.
Therefore, the required sample size is:
[tex]n=0.65(1-0.65) \left(\frac{2.576}{0.02} \right)^{2}[/tex]
[tex]=0.2275 \times 16589.44[/tex]
[tex]=3774.1 \approx 3774[/tex]
Therefore, the required sample size is 3774
