5 Records on a fleet of trucks reveal that the average life

5. Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles. To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   22100  
Ha:    u   =/   22100  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    17          
tcrit =    +/-   2.109815578      
              
Getting the test statistic, as              
              
X = sample mean =    23400          
uo = hypothesized mean =    22100          
n = sample size =    18          
s = standard deviation =    1412          
              
Thus, t = (X - uo) * sqrt(n) / s =    3.906113947          
              
Also, the p value is, as it is two tailed,              
              
p =    0.001136521          
              
Comparing |t| > 2.1098, (or, p < 0.05), we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the mean average life is not 22,100 miles. [CONCLUSION]