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In the past year, 15% of all garments made in a factory had a defect of some kind. To reduce the proportion of defective garments, the factory manager offers a $100 bonus for each employee if she finds convincing evidence that the proportion of defective garments produced during the next month is less than 0.15. At the end of the month, the manager selects a random sample of 200 garments and finds that 26 of them have a defect.
Assume that the offer has no effect on the proportion of defective garments.
-(a) What is the shape of the sampling distribution of the sample proportion of defective garments for random samples of size 200? How do you know?
-(b) Find the mean and standard deviation of the sampling distribution of the sample proportion of defective garments for random samples of size 200.
-(c) Calculate the probability of getting a sample proportion of defective garments of 26/200 or less. (d) Based on your previous answers, is there convincing evidence that the proportion of garments produced this month with defects is less than 0.15? Explain.
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