Hello The average gasoline price of one of the major oil com

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.

Solution

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]