Question

A marketing research company desires to know the mean consumption of milk per week among people over age 3030. They believe that the milk consumption has a mean of 3.53.5 liters, and want to construct a 85%85% confidence interval with a maximum error of 0.070.07 liters. Assuming a standard deviation of 1.41.4 liters, what is the minimum number of people over age 3030 they must include in their sample? Round your answer up to the next integer.

I do not understand how to solve it. What formulas do I use? What chart do I use?

Answer 1

Solution :

Given that,

Population standard deviation = = 1.4

Margin of error = E = 0.07

At 85% confidence level the z is,

= 1 - 85%

= 1 - 0.85 = 0.15

/2 = 0.075

Z/2 = Z0.075 = 1.44 ( Using standard normal table)

sample size = n = [Z/2* / E] 2

n = [1.44 * 1.4 / 0.07]2

n = 829.44

Sample size = n = 830 peoples