Answer:
The minimum number of people over age 45 they must include in their sample is 305.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 0.6 liters
This means that [tex]\sigma = 0.6[/tex]
What is the minimum number of people over age 45 they must include in their sample?
This is n for which M = 0.08. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.08 = 2.327\frac{0.6}{\sqrt{n}}[/tex]
[tex]0.08\sqrt{n} = 2.327*0.6[/tex]
[tex]\sqrt{n} = \frac{2.327*0.6}{0.08}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*0.6}{0.08})^2[/tex]
[tex]n = 304.6[/tex]
Rounding up:
The minimum number of people over age 45 they must include in their sample is 305.
