Question

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.94. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $0.20 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 your answers up to the nearest whole number.)

(a) The desired margin of error is $0.10. ______

(b) The desired margin of error is $0.06. _________

(c) The desired margin of error is $0.05. ________

Answer 1

Solution:

Given ,

= 0.20

c = 95% = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025

Using Z table ,

= 1.96

a)

Here , E = 0.10

Now, sample size (n) is given by,

=  {(1.96* 0.20)/0.10}²

=  15.3664

= 16 ..(round to the next whole number)

Answer : Required Sample size is n = 16

b)

Here , E = 0.06

Now, sample size (n) is given by,

=  {(1.96* 0.20)/0.06}²

=  42.6844444444

= 43 ..(round to the next whole number)

Answer : Required Sample size is n = 43

c)

Here , E = 0.05

Now, sample size (n) is given by,

=  {(1.96* 0.20)/0.05}²

=  61.4656

= 62 ..(round to the next whole number)

Answer : Required Sample size is n = 62