Question

A research company desires to know the mean consumption of milk per week among people over age 20. They believe that the milk consumption has a mean of 4.5 liters and want to construct a 99% confidence interval with a maximum error of 0.09 liters. Assuming a standard deviation of 1.2 liters, what is the minimum number of people over age 20 they must include in their sample?

a. 37
b. 41
c. 45
d. 49

Answer 1

The minimum sample size needed for the given requirements is 1181 individuals, which means there must be an error in the provided options as they are all too low.

Step-by-step explanation:

To solve for the minimum number of people needed for the sampling distribution to achieve a 99% confidence interval with a maximum error (E) of 0.09 liters, where the population standard deviation (σ) is assumed to be 1.2 liters, we use the formula for sample size:

n = (Z*σ/E)^2

For a 99% confidence interval, the Z-score that corresponds to the middle 99% is approximately 2.576. Plugging the values into the equation yields:

n = (2.576*1.2/0.09)^2

= (2.576*13.33)^2

= (34.35)^2

= 1180.02

Since we cannot have a fraction of a person, we round up to the nearest whole number, which means the minimum sample size (n) is 1181 individuals.

The options provided (37, 41, 45, 49) are all too small compared to the calculated minimum sample size. It appears there is a mistake in the options listed, as none of them are correct based on the given parameters.