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 $.09 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 $.05 The appropriate sample size is ____.

Answer 1

Solution :

Given that,

standard deviation = = 0.24

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

(a)

margin of error = E = 0.09

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 0.24) / 0.09)²

= 27.31 = 28

The appropriate sample size is 28

(b)

margin of error = E = 0.06

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 0.24) / 0.06)²

= 61.46 = 62

The appropriate sample size is 62 .

(c)

margin of error = E = 0.05

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 0.24) / 0.05)²

= 88.51 = 89

The appropriate sample size is 89 .