Question

The manufacturer of a new race car engine claims that the proportion of engine failures due to overheating for this new engine, (p1), will be no higher than the proportion of engine failures due to overheating of the old engines, (p2). To test this statement, NASCAR took a random sample of 140 of the new race car engines and 145 of the old engines. They found that 14 of the new race car engines and 11 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 race car engine? Use a significance level of α=0.05 for the test.

Step 1 of 6 :  State the null and alternative hypotheses for the test.

Step 2 of 6 : Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 3 of 6 : Compute the weighted estimate of p, p‾. Round your answer to three decimal places.

Step 5 of 6 :

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

Answer if you reject or fail to reject the null hypothesis and if there is or isn't sufficient evidence to support the claim

Answer 1

(claim)

Test statistic:

P-value> Significance

Do not reject Null hypothesis

Hence,

State the null and alternative hypotheses for the test.

(claim)

Find the values of the two sample proportions, pˆ1 and pˆ2

p^1=0.100

p^2=0.076

Compute the weighted estimate of p

p^=0.088

Find the P-value for the hypothesis test

0.2358

fail to reject the null hypothesis and there isn't sufficient evidence to support the claim.