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 115115 of the new racecar engines and 165165 of the old engines. They found that 1212 of the new racecar engines and 66 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 1 of 6 :  

State the null and alternative hypotheses for the test.

state the sample proportions

state the value of the t test

the value of p

reject or fail, reason

Answer 1

a).hypothesis:-

the manufacturer's claim is the null hypothesis.

b).given data and necessary calculations of sample proportions are:-

c).the pooled proportion be:-

d). test statistic is:-

e).the p value is :-

f).decision:-

p value = 0.0000 < 0.01 (alpha)

we reject the null hypothesis and we can say that, NASCAR have enough evidence to reject the manufacturer's claim about the new racecar engine at 0.05 level of significance.