you are the automotive specialist for the monthly magazine p

you are the automotive specialist for the monthly magazine. part of your jobs is to investigate the claims made by automakers in commercails. you are suspious of a new economy care that auotmaker claims will get 78 miles per gallon, after checking the milage figures for a random sample of 125 owners of this car you find an average miles per gallon of 75.5 with a standard deviation of 3.7. at the 99% level do your results tend to confirm or refute manufactor\'s claims?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   78  
Ha:    u   =/   78  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          
zcrit =    +/-   2.575829304      
              
Getting the test statistic, as              
              
X = sample mean =    75.5          
uo = hypothesized mean =    78          
n = sample size =    125          
s = standard deviation =    3.7          
              
Thus, z = (X - uo) * sqrt(n) / s =    -7.554283708                  
              
As z is not between the two critical z values, we REJECT THE NULL HYPOTHESIS.          

Thusm there is significant evidence that the mean is not 78 miles per gallon. We can refute the manufacturer\'s claims. [CONCLUSION]