Question

A marketing research company desires to know the mean consumption of meat per week among people over age 49

. They believe that the meat consumption has a mean of 4.2
pounds, and want to construct a 90%
confidence interval with a maximum error of 0.06
pounds. Assuming a variance of 1.44
pounds, what is the minimum number of people over age 49
they must include in their sample? Round your answer up to the next integer.

Answer 1

To calculate the minimum sample size required to construct a 90% confidence interval with a maximum error of 0.06 pounds, we can use the formula:

n = (Z^2 * σ^2) / E^2

where n is the sample size, Z is the z-score corresponding to the desired confidence level (in this case, 90%), σ^2 is the variance, and E is the maximum error.

Substituting the given values, we get:

n = (1.645^2 * 1.44) / 0.06^2

n = 84.934

Rounding up to the next integer, we get a minimum sample size of 85 people over age 49.

Therefore, the marketing research company must include at least 85 people over age 49 in their sample to construct a 90% confidence interval with a maximum error of 0.06 pounds, assuming a variance of 1.44 pounds and a mean consumption of meat per week of 4.2 pounds.