Question

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.95. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.24 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. Round up to the next whole number.

a. The desired margin of error is $.10. The appropriate sample size is ____.

b. The desired margin of error is $.06. The appropriate sample size is ____.

c. The desired margin of error is $.04. The appropriate sample size is _____.

Answer 1

Solution :

Given that,

a.)

standard deviation = = $0.24

margin of error = E = $0.10

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 *0.24 ) / 0.10)²

= 22.13

Sample size =23

b.)

standard deviation = = $0.24

margin of error = E = $0.06

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 *0.24 ) / 0.06)²

= 61.47

Sample size = 62

c.)

standard deviation = = $0.24

margin of error = E = $0.04

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

  = ((1.96 *0.24 ) / 0.04)²

= 138.30

Sample size = 139