Question

The manufacturer of a new racecar 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 170 170 of the new racecar engines and 130 of the old engines. They found that 17 of the new racecar engines and 6 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=0.1 for the test.

1. State the null and alternative hypotheses for the test.

2. Find the values of the two sample proportions, pˆ1and pˆ2. Round your answers to three decimal places.

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

4. Compute the value of the test statistic. Round your answer to two decimal places.

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

6.Make the decision to reject or fail to reject the null hypothesis.

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

2)

p1cap = X1/N1 = 17/170 = 0.1
p2cap = X2/N2 = 6/130 = 0.046

3)

pcap = (X1 + X2)/(N1 + N2) = (17+6)/(170+130) = 0.077

4)

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1-0.046)/sqrt(0.077*(1-0.077)*(1/170 + 1/130))
z = 1.74

5)

P-value Approach
P-value = 0.0409

6)

As P-value < 0.1, reject the null hypothesis.