Question

A consumer magazine polls car owners to see if they are happy with their vehicles and would purchase the same model again. They randomly selected car owners and found the following: 429 of 550 owners of Japanese models would purchase their vehicle again, and 324 of 450 owners of American-made cars would purchase the same model again.

a) Check the assumptions and conditions for comparing proportions.

b) Find a 95% confidence interval (Two-Proportion z-Interval) for the difference in the proportions.

c) Interpret your interval in the context of the problem. What does the confidence interval say about the difference in the satisfaction of the two types of owners (hint: pay attention to the signs on the LB & UB)?

d) Conduct a hypothesis test with an alpha-level of 0.05 to determine if there is strong evidence that owners of Japanese-made cars are happier with their purchase than owners of American-made cars. (Be sure to give the name of the test that you are performing.)

e) If your conclusion is wrong, what type of error did you make?

Answer 1

c) Here the confidence interval does not contain 0. Thus there is sufficient evidence that there is difference in the satisfaction of two types of owners.

d) we are performing two sample proportion z test. Here we reject Ho. Thus there is sufficient evidence that owner of Japanese made cars are happier than the owners of American made cars.

e) if the conclusion is wrong, we would make type 1 error.. Because we are concluding that Ho should be rejected... So rejecting Ho when Ho is true is type 1 error.