The average gasoline price of one of the major oil companies has been $3.00 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 $3.06. assume that the standard deviation of the population is $0.09. exam review 3 2

(a) state the null and the alternative hypothesis.
(b) test the claim at α = 0.05.
(c) what is the p-value associated with the above sample results

(a) vs (upper-tail alternative)

(b) We reject the null hypothesis at the significance level of 0.05.

(c) The p-value is 3.167124e-05

Step-by-step explanation:

vs (upper-tail alternative)

We have , and n = 36. We have a large sample and our test statistic is

which shoud be normal standard when is true. We have observed

.

We should use the significance level . The 95th quantile of the standard normal distribution is and the rejection region is given by RR = {z | z > 1.6449}. Because the observed value 4 is greter than 1.6449, we reject the null hypothesis at the significance level of 0.05.

The p-value is computed as P(Z > 4) = 3.167124e-05