Question

Historically, general motors reports that 70 percent of leased vehicles are returned with less than 36,000 miles. a recent sample of 200 vehicles returned at the end of their lease showed 158 had less than 36,000 miles. has the proportion increased?

Answer 1

Yes, the proportion of leased vehicles returned with less than 36,000 miles has increased.

Step-by-step explanation:

To determine if the proportion of leased vehicles returned with less than 36,000 miles has increased, we can perform a hypothesis test. Let's assume that the historical proportion of vehicles returned with less than 36,000 miles is still 70%. Our null hypothesis (H0) is that the proportion has not increased, while the alternative hypothesis (Ha) is that the proportion has increased. We can use a one-proportion z-test to test this. Using the sample data, we find that out of 200 vehicles returned, 158 had less than 36,000 miles. This gives us a sample proportion of 158/200 = 0.79. To test the hypothesis, we calculate the test statistic:

z = (0.79 - 0.70) / sqrt((0.70 * (1-0.70)) / 200) = 3.67

Using a significance level of alpha = 0.05, we compare the test statistic to the critical value for a one-tailed test. The critical value for a 95% confidence level is approximately 1.645. Since 3.67 > 1.645, we reject the null hypothesis and conclude that the proportion of leased vehicles returned with less than 36,000 miles has increased.