The owner of a gasoline station wants to study gasoline purc

The owner of a gasoline station wants to study gasoline purchasing habits of his customers. He selects a random sample of 64 motorist during a week with the following results: x =10.5 gallons;s=1.5 gallons. Can we conclude that the average amount of gasoline purchased at his station is greater than 10 gallons? Use a significance level of 0.01.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   10  
Ha:    u   >   10  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    +   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    10.5          
uo = hypothesized mean =    10          
n = sample size =    64          
s = standard deviation =    1.5          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.666666667          
              
Also, the p value is              
              
p =    0.003830381          
              
As |z| > 2.326, and P < 0.01, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the average amount of gasoline purchased at his station is greater than 10 gallons. [CONCLUSION]