Question

The manufacturer of a new racecar engine claims that the proportion of engine failures due to overheating for this new engine, (p1)(p1), will be no higher than the proportion of engine failures due to overheating of the old engines, (p2)(p2). To test this statement, NASCAR took a random sample of 135135 of the new racecar engines and 175175 of the old engines. They found that 1414 of the new racecar engines and 88 of the old engines failed due to overheating during the test. Does NASCAR have enough evidence to reject the manufacturer's claim about the new racecar engine? Use a significance level of α=0.01α=0.01 for the test.

Step 5 of 6 :

Find the P-value for the hypothesis test. Round your answer to four decimal places.

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 <   0          
                  
sample #1   ----->              
first sample size,     n1=   135          
number of successes, sample 1 =     x1=   14          
proportion success of sample 1 , p̂1=   x1/n1=   0.1037          
                  
sample #2   ----->              
second sample size,     n2 =    175          
number of successes, sample 2 =     x2 =    88          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.5029          
                  
difference in sample proportions, p̂1 - p̂2 =     0.1037   -   0.5029   =   -0.3992
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.3290          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.05382          
Z-statistic = (p̂1 - p̂2)/SE = (   -0.399   /   0.0538   ) =   -7.4161
                  
p-value =        0.0000   [Excel function =NORMSDIST(z)      
decision :    p-value<α,Reject null hypothesis