A marketing research company desires to know the mean consumption of milk per week among people over age 45. They believe that the milk consumption has a mean of 4.2 liters, and…

Question

asked Jan 13, 2022 148k views

1 Answer

Busybear · Answer 1 · 2022-01-16T18:57:37+0000

Answer:

The minimum number of people over age 45 they must include in their sample is 305.

Explanation:

We have that to find our
$\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1 - 0.98)/(2) = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of
$1 - \alpha$ .

That is z with a pvalue of
1 - 0.01 = 0.99 , so Z = 2.327.

Now, find the margin of error M as such

$M = z(\sigma)/(√(n))$

In which
$\sigma$ is the standard deviation of the population and n is the size of the sample.

Standard deviation of 0.6 liters

This means that
$\sigma = 0.6$

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

$M = z(\sigma)/(√(n))$

0.08 = 2.327(0.6)/(√(n))

0.08√(n) = 2.327*0.6

√(n) = (2.327*0.6)/(0.08)

(√(n))^2 = ((2.327*0.6)/(0.08))^2

n = 304.6

Rounding up:

The minimum number of people over age 45 they must include in their sample is 305.