Please answer Statistics problem 2?

[vipponah]

When a law firm represents a group of people in class action lawsuit and wins that lawsuit, the firm receives a percentage of the group's monetary settlement. That settlement amount is based on the total number of people in the group- the large the group and the large the settlements, the more money firm will receive. A law firm is trying to decide whether to represent car owners in a class action lawsuit against the manufacturer of a certain make and model for a particular defect. If 5% 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 the defect. The firm plans to take a random sample of 1000 people who bought this car and ask them if they experienced this defect in their cars.

a. Define the parameter of interest and state the null and alternative hypotheses that the law firm should test.
b. In the context of this situation, describe Type I and Type II errors and descrive the consequences of each of these for the law firm.

Please show work and really do thank you.

[anglesey34]

a)
Parameter of interest: proportion of all defective cars of the model under lawsuit
H0: proportion of all of 'this' defective cars <= 0.05
Ha: proportion of all of 'this' defective cars > 0.05

b)
Type I error : reject the null hypothesis when it is true. When the true proportion of defective cars is less than 5%, it was decided that the proportion of defectives is more than 5%. This would result in the firm not being able to recover its expenses.

Type II error:
Do not reject H0 when H1 is true.
When the true proportion of defective cars exceeded 5%, the firm has decided that it was less than 5% and wouldn't have handled the lawsuit. This again means loss of money which the firm would have earned had it taken the case. However, there would have been no expenses for the firm.