1. A law firm receives a percent of the monetary settlement of a client when the law form represents the client in a class action lawsuit and wins the lawsuit. The law firm is trying to decide whether to represent a group of car owners in a class action lawsuit against the manufacturer of a certain make and model for a particular defect. If 5 percent or less of the cars of this make and model have the defect, the firm will not recover its expenses. Therefore, the firm will handle the lawsuit only if it is convinced that more than 5% of cars of this make and model have defect. The firm takes a random sample of 1000 people who bought this car and asked them if they experienced this defect in their cars. 6.2% said yes.

1. Is there convincing evidence that more than 5 percent of cars of this make and model have defect at a significance level of 0.05? Explain.
2. Calculate and interpret a 95% confidence interval to estimate the proportion of car owners that said thy experienced the defect in their car.
3. Explain why the result from confidence interval is not consistent with the result from the test for significance.
4. In the context of this situation, describe Type I and Type II errors and describe the consequences of each of these for the law firm.