Question

An automobile manufacturer claims that their jeep has a 34.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep. After testing 250 jeeps they found a mean MPG of 35.0. Assume the standard deviation is known to be 1.6. Is there sufficient evidence at the 0.02 level that the jeeps have an incorrect manufacturer's MPG rating?

Step 4 of 5: Enter the decision rule.

Answer 1

Ho :   µ =   34.7                  
Ha :   µ ╪   34.7       (Two tail test)          
                          
Level of Significance ,    α =    0.020                  
population std dev ,    σ =    1.6000                  
Sample Size ,   n =    250                  
Sample Mean,    x̅ =   35.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   1.6000   / √    250   =   0.1012      
Z-test statistic= (x̅ - µ )/SE = (   35.000   -   34.7   ) /    0.1012   =   2.965
                          
  
p-Value   =   0.0030   [ Excel formula =NORMSDIST(z) ]  

          
Decision:   p-value<α, Reject null hypothesis

conclusion:   there is sufficient evidence at the 0.02 level that the jeeps have an incorrect manufacturer's MPG rating