The quality control department of Widgets Manufacturing needs your help. They can’t decide which significance level is appropriate for testing the claim that fewer than 50% of widgets from a production run are defective. One group feels that the primary consideration for choosing between alpha=0.01 and alpha=0.05 should be to keep the rejection rate of good widgets as small as possible, while the other group feels they should try to keep the number of defective widgets that make it through to a minimum. Write two paragraphs detailing the arguments might each group make to support their position. Your paragraphs should include the terms alternative hypothesis, Type I error, Type II error, sample size and power. Keeping in mind that this is a serious life threatening disease which significance level would you choose? In a sample of 1500 widgets it is found that 679 are defective. Test the claim at the significance level you chose and state your conclusion in non-technical terms.
Format and Hint: This is a proportion problem. For parts 1-5, you need to find the point estimate p-hat and then use the proportion formula. You do not need to show all your work. For this problem, I am only interested in your final confidence intervals and your respond to the discussion question. Once again remember that I will be grading your emails and not your posts.
Scenario: A hotel has decided that to cut costs, it will outsource its reservation business to another company. The other company claims that it can convert 65% of all incoming calls into reservations for the hotel. The compensation for the outsourcing company is based upon their claimed conversion rate. In an effort to determine if they are getting their money’s worth from the outsourcing company, the hotel decides to take some samples of calls to see what percentage of reservations is made. Find the 95% Confidence Interval for the proportion based upon the following samples.
1. Twenty calls resulting in eleven reservations (n = 20 and x = 11).
2. 210 calls with 124 reservations
3. 400 calls with 240 reservations
4. x = 781 and n = 1280
5. x = 2460 and n = 4000
Discussion Question: At what point do we start to doubt the claims of the outsourcing company? Do you think the outsourcing company is delivering on their promise?
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