The Lundberg Survey monitors gas prices at gas stations nationwide. In a recent

Question

The Lundberg Survey monitors gas prices at gas stations nationwide. In a recent month, Lundberg reported that the average regular gas price for the stations it surveyed was $3.506 per gallon (source : lundbergsurvey.com). Assume the population distribution of gas prices is normal. If the sample size was 20 stations and the standard deviation of gas prices in the sample was $.16,

a. build a 95% confidence interval estimate of the average price of a gallon of gas for the population of gas stations nationwide.

b. If the size of the sample was 10 instead of 20, show the 95% confidence interval estimate

Explanation / Answer

Solution:-

Given,

Mean = $3.506 per gallon

Sample size = 20

Standard deviation = $ 0.16

a). Build a 95% confidence interval estimate of the average price of a gallon of gas for the population of gas stations nationwide.

Calculation

M = 3.506
t = 1.96
sM = (0.162/20) = 0.04

= M ± Z(sM)
= 3.506 ± 1.96*0.04
= 3.506 ± 0.07012

95% CI [3.43588, 3.57612].

You can be 95% confident that the population mean () falls between 3.43588 and 3.57612.

b. If the size of the sample was 10 instead of 20, show the 95% confidence interval estimate.

Calculation

M = 3.506
t = 1.96
sM = (0.162/10) = 0.05

= M ± Z(sM)
= 3.506 ± 1.96*0.05
= 3.506 ± 0.09917

95% CI [3.40683, 3.60517].

You can be 95% confident that the population mean () falls between 3.40683 and 3.60517.

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