Respuesta :
Answer:
You must test a sample size of at least 514 Americans.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex] is the margin of error.
95% confidence interval
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
We have that:
[tex]M = 0.03, \pi = 0.14[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.14*0.86}{n}}[/tex]
[tex]0.03\sqrt{n} = 0.68[/tex]
[tex]\sqrt{n} = 22.67[/tex]
[tex]n = 513.92[/tex]
You must test a sample size of at least 514 Americans.
Answer:
Sample size of at least 514 Americans is required.
Step-by-step explanation:
We are given that the soap taste is inherited through the olfactory receptor gene OR6A2. About 14% of the population has this gene.
Let p = % of population having this gene = 0.14
Also, Margin of error = 3%
Confidence level = 95%
Margin of error formula = [tex]Z_\frac{\alpha}{2} * \frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]Z_\frac{\alpha}{2}[/tex] = At 5% level of significance z score has value of 1.96
[tex]\sigma[/tex] = [tex]\sqrt{p(1-p)}[/tex] = [tex]\sqrt{0.14 * 0.86}[/tex] = 0.347
So, Margin of error = [tex]1.96* \frac{\sqrt{0.14*0.86} }{\sqrt{n} }[/tex]
[tex]\sqrt{n}[/tex] = [tex]\frac{1.96*0.347}{0.03}[/tex]
n = [tex]22.671^{2}[/tex] = 513.95 ≈ 514
Therefore, sample must be of 514 Americans .
