1. The average gasoline price of one of the major oil companies has been $1.00 p

Question

1. The average gasoline price of one of the major oil companies has been $1.00 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 $1.10. Assume that the standard deviation of the population () 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?

Explanation / Answer

Note that _x= /n= 0.12 /36= 0.02

a.H0:1Ha:1

It is a one tailed test because we think that the results of the shortage is anincrease.

b.z= (– ) / _x= (1.10 – 1) / 0.02 = 5; therefore, reject H0,

there is sufficientevidence at= .05 to conclude that there has been an increase in the averageprice.We know this for two reasons.The critical value we compare our Z to is 1.96.

If it is significantly larger than1.96 then we think the price is much higher.We can also use the p-value method.If our p-value of our test stat is smaller than= .05,

then we reject Ho and conclude there is a statistically significant resultand in this case suspect the price of gas has increased.The p-value of Z = 5 is< 0.001.

So this is much less than 0.05

c.almost zero< 0.001 because it is smaller than the last computed table value

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