Question

The manufacturer of a new racecar engine claims that the proportion of engine failures due to overheating for this new engine, (p), will be no higher than the proportion of engine failures due to overheating of the old engines, (p). To test this statement, NASCAR took a random sample of 235 of the new racecar engines and 190 of the old engines. They found that 24 of the new racecar engines and I l 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 a = 0.1 for the test. Step 4 of 6: Compute the value of the test statistic. Round your answer to two decimal places

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 >   0          
                  
sample #1   ----->   experimental          
first sample size,     n1=   235          
number of successes, sample 1 =     x1=   24          
proportion success of sample 1 , p̂1=   x1/n1=   0.1021          
                  
sample #2   ----->   standard          
second sample size,     n2 =    190          
number of successes, sample 2 =     x2 =    11          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.058          
                  
difference in sample proportions, p̂1 - p̂2 =     0.1021   -   0.0579   =   0.0442
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.082   
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0268          
Z-statistic = (p̂1 - p̂2)/SE = (   0.044   /   0.0268   ) =   1.65

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