Question

A consumer report claims that more than 10% of the cars from a car manufacture experience engine failures before reaching a mileage of 150,000 miles. A sample of 65 cars is investigated and 9 of the cars had engine failure before 150,00 miles. Conduct a hypothesis test to test the claim with a significance level of 0.10.

Answer 1

We will fail to reject the null hypothesis and conclude that there is no sufficient evidence to suggest that more than 10% of the cars from a car manufacture experience engine failures before reaching a mileage of 150,000 miles

Explanation:

We are given;

Population proportion; p_o = 10% = 0.1

Sample proportion; p = 9/65 = 0.1385

Z-score formula for this is;

z = (p - p_o)/√(p_o(1 - p_o)/n)

z = (0.1385 - 0.1)/√(0.1(1 - 0.1)/65)

z = 0.0385/0.0372

z = 1.03

From online z-score calculator, we have; p - value = 0.1504

Our p - value is greater than the significance level of 0.1.

Thus,we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to suggest that more than 10% of the cars from a car manufacture experience engine failures before reaching a mileage of 150,000 miles