According to the U.S. federal Highway Administration, the mean number of miles d

Question

According to the U.S. federal Highway Administration, the mean number of miles driven annually is µ=12,200. An insurance agent in Montana believes that the mean number of miles driven by the residents of his stat is higher than the national average. A random sample of 35 drivers is taken from the list of registered drivers in the state of Montana. The mean number of miles driven by the 35 drivers is 12,895. Assuming the population standard deviation, = 3800 miles, test the agent’s claim at the 1% level of significance.

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   12200  
Ha:    u   >   12200  
              
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 =    12895          
uo = hypothesized mean =    12200          
n = sample size =    35          
s = standard deviation =    3800          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.082019855          
              
Also, the p value is              
              
p =    0.139621853          
              
As z < 2.33, and P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

There is no significant evidence that the mean number of miles driven by the residents of his state is higher than the national average. [CONCLUSION]

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