Question

a marketing research company desires to know the mean consumption of potatoes per week among people over age 49. They believe that potatoes consumption has a mean of 4.2 pounds and want to construct a 95% confidence interval with a maximum error of .05 pounds. Assuming a variance of 1.44 pounds, what is the minimum number of people over age 49 they must include in their sample?

A)1960

B)2401

C)49

D)2213

E)297

Answer 1

Solution :

Given that,

variance = 2 = 1.44

Population standard deviation = = 2 = 1.44 = 1.2

Margin of error = E = 0.05

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96  

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

n = [1.96 * 1.2 / 0.05 ]2

n = 2212.76

Sample size = n = 2213

correct option is = D