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 $0.25 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 $0.04.

Answer 1

Solution :

Given that,

Population standard deviation = = 0.25

a) Margin of error = E = 0.10

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z0.025 = 1.960

Z/2 = 1.960  

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

n = [ 1.96 *0.25/0.10 ]2

n = 24

Sample size = n = 24

b)

Margin of error = E = 0.06

Z/2 = 1.960  

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

n = [ 1.96 *0.25/0.06 ]2

n = 67

Sample size = n = 67

c)

Margin of error = E = 0.04

Z/2 = 1.960  

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

n = [ 1.96 *0.25/0.04 ]2

n = 150

Sample size = n = 150