1The average gasoline price of one of the major oil companie

1-The average gasoline price of one of the major oil companies has been $2.50 per gallon. Because of shortages in production of crude oil, it is believed that there has been a significant increase in the average price. In order to test this belief, we randomly selected a sample of 36 of the company’s gas stations and determined that the average price for the stations in the sample was $2.60. Assume that the standard deviation of the population (s) is $0.12.

a. State the null and the alternative hypotheses.

b. Test the claim at = .05. c. What is the p-value associated with the above sample results?

d. State your conclusion.

Solution

Set Up Hypothesis
Null, No change in Price H0: U = 2.5
Alternate, significant increase in the average price H1: U>2.5
Test Statistic
Population Mean(U)=2.5
Given That X(Mean)=2.6
Standard Deviation(S.D)=0.12
Number (n)=36
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=2.6-2.5/(0.12/Sqrt(36)
Zo =1.75
| Zo | =1.75
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.75 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 1.75 ) = 0.0401
Hence Value of P0.05 > 0.0401, Here we Reject Ho

We conclude that there is significant increase in the average price