Question

An owner of a gas station chain claimed that there was no difference in gas prices between gas stations on the east coast and gas stations on the west coast. A skeptical consumer believed that prices on the east coast were higher. The consumer collected two samples from both coasts. In the east coast sample, the sample size was 45 and the average price was $2.45 per gallon. The population standard deviation for east coast gas prices is believed to be $0.55. In the west coast sample, the sample size was 55 and the average price was $2.32 per gallon. The population standard deviation for west coast gas prices is believed to be $0.52. With alpha equal to 0.05, test the claim.

Answer 1

H0: 1 - 2 = 0

Ha: 1 - 2 0

Test Statistic :-

Z = ( 2.45 - 2.32 ) / sqrt{( 0.552 /45 ) + ( 0.522 /55 )}

Z = 1.21

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2)
Critical value Z(α/2) = Z(0.05 /2) = 1.96

| Z | > Z(α/2) = 1.205 < 1.96

Result :- Fail to Reject Null Hypothesis

We do not have sufficient evidence to support the claim