Question

Suppose a marketing director of a supermarket chain would like to estimate the population-mean sales of a new cereal within + $20 with 99% confidence. If the population standard deviation is assumed to be $120, what sample size is needed? What would be your sample size if your population is 3000?

Show work please

Answer 1

Solution:

The sample size formula is given as below:

n = (Z*σ/E)^2

We are given

Population standard deviation = σ = 120

Confidence level = 99%

Critical Z value = 2.5758

(by using z-table)

Margin of error = E = 20

The sample size is given as below:

n = (Z*σ/E)^2

n = (2.5758*120/20)^2

n = 238.8508

n = 239

Required sample size = 239

This sample size is greater than 5% of 3000, so sample size would be 239 if population size is 3000.