Question

3. The general manager for United Meat Producers is interested in estimating the mean pounds of hamburgers that are purchased per month by households in Philadelphia, PA. To determine the required sample size, she would like her estimate to be within plus or minus 0.50 pounds per month, and she like to estimate to be at the 99% confidence level. Assume that the standard deviation for hamburger purchases is σ = 4 pounds. Use the information provided to determine the required sample size for this study

Answer 1

3)

Solution :

Given that,

Population standard deviation = = 4

Margin of error = E = 0.50

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z_/2* / E) ²

n = (2.576 * 4 / 0.50)²

n = 424.7

n = 425

Sample size = 425