Hello, The average gasoline price of one of the major oil companies has been $2.
ID: 3380196 • Letter: H
Question
Hello,
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.
Explain each step please:
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.
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 2.5
Ha: u > 2.5 [ANSWER]
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b)
As we can see, this is a right tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = + 1.644853627
Getting the test statistic, as
X = sample mean = 2.6
uo = hypothesized mean = 2.5
n = sample size = 36
s = standard deviation = 0.12
Thus, z = (X - uo) * sqrt(n) / s = 5
Comparing z > 1.6449, we REJECT THE NULL HYPOTHESIS. [DECISION]
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c)
Also, the p value is
p = 0.000000286652 [ANSWER]
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d)
Thus, there is significant evidence that the mean price of crude oil increased. [CONCLUSION]
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