Question

Roland was driving to campus but realized that his car is out of gas. He started driving around Syracuse looking for a gas station and comparing their gas prices, searching for the cheapest one. He drove by 50 different gas stations. He computed their average gas price to be $2.74 per gallon. Last year around the same time in November, the average gas price in the entire of Syracuse was $2.68 per gallon with the standard deviation of $0.11. Let's assume that the standard deviation hasn't changed since last year. Roland called his mom: Roland: "Mom, did you know that average gas prices have gone up since the same time last year?" Mom: "Are you sure, Roland?" Roland: "Yes, mom, 95% sure." Mom: "I don't think you're right." Who is right? Mom is right Roland is right

Answer 1

Roland is right, he can be 95% sure that average gas prices have gone up since the same time last year.

Explanation:

Let μ be average gas price around Syracuse.

Then hypotheses are:

`H_(0):` μ = $2.68

`H_(a):` μ > $2.68

Then test statistic can be calculated as:

z=
`(X-M)/((s)/(√(N) ) )` where

• X is the Roland's calculated average gas prices of 50 gas stations ($2.74)

• M is the average average gas prices in the entire of Syracuse last year

• s is the standard deviation ($0.11)

• N is the sample size(50)

Then z=
`(2.74-2.68)/((0.11)/(√(50) ) )` ≈ 3.86

Since P-value of test statistic ≈ 0.00006 <0.05 (significance level), we can reject the null hypothesis.