Question

New York State claims that the average cost for gasoline is less than $2.60 per gallon. You think this information is incorrect, so you travel to 41 different gas stations and find that the mean cost of gas is $2.57 per gallon. Assume the population standard deviation is $0.25 per gallon. Is there enough evidence to support the claim for ? = 0.01? Be sure to identify the null and alternative hypotheses.

Answer 1

Null and alternative hypotheses

Ho : = 2.60

H1 : < 2.60

Level of significance a = 0.01

Test statistic Z

Z = ( xbar - )/(/√n)

Z = ( 2.57 - 2.60)/(0.25/√41)

Z test statistic = -0.77

Zcritical for a = 0.01 and left tailed test

Zcritical = Z​​​​​​a = Z​​​​​​0.01

Zcritical = -2.33

Decision rule : if Z test statistic < -2.33 , we reject the null hypothesis otherwise we fail to reject the null hypothesis

Out Z = -0.77 > -2.33

Conclusion : Fail to reject the null hypothesis. There is no sufficient evidence to support the claims that the average cost for gasoline is less than $2.60 per gallon