The manufacturer of a metal stand for home TV sets must be sure that its product
ID: 3294540 • Letter: T
Question
The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300300 pounds, the company's safety inspectors have set a standard of ensuring that the stand can support an average of over 475 pounds. Their inspectors regularly subject a random sample of the stands to increasing weight until they fail. They test the hypothesis Upper H 0H0: muequals=475 against Upper H Subscript Upper AHA: mugreater than>475, using the level of significance alphaequals=0.01. If the sample of stands fails to pass this safety test, the inspectors will not certify the product for sale to the general public. The manufacturer is thinking of revising its safety test. Complete parts a through c below.
a) If the company's lawyers are worried about being sued for selling an unsafe product, should they make the value of alpha smaller or larger? Explain. Choose the correct answer below. A. They should make the value of alpha smaller. This means a smaller chance of declaring the stands safe when they are not actually safe. B. They should make the value of alpha larger. This means a smaller chance of declaring the stands safe when they are not actually safe. C. They should make the value of alpha larger. This means a smaller chance of declaring the stands unsafe when they are actually safe. D. They should make the value of alpha smaller. This means a smaller chance of declaring the stands unsafe when they are actually safe.
b) In this context, what is meant by the power of the test? A. The probability of correctly detecting that the stands are not capable of holding more than 475475 pounds. B. The probability of incorrectly detecting that the stands are not capable of holding more than 475475 pounds. C. The probability of correctly detecting that the stands are capable of holding more than 475 pounds. D. The probability of incorrectly detecting that the stands are capable of holding more than 475475 pounds.
c) If the company wants to increase the power of the test, what options does it have? Explain the advantages and disadvantages of each option. Select all that apply. A. The company could increase the "design load" to be well above 475 pounds. This would probably be costly. B. The company could increase the sample size. This would take more time for testing and be costly. C. The company could change the production procedure so that the standard deviation of the weights of the stands decreases. This would probably be costly. D. The company could increase alpha. This would result in more Type I errors.
Explanation / Answer
a. The company will be sued, if the products they are selling are found to be unsafe. The products will be found unsafe, if the null hypothesis is rejected. Therefore, the lawyers will try not to reject null hypothesis. Thus, they will decrease the value of alpha. This discards options B and C. Among option A and D, option D is correct, because increasing the alpha means smaller chance of declaring the products unsafe.
b. The power of a test refer to likelihood of rejecting a false null hypothesis, that is correctly rejecting the null hypothesis, when it is false. Thus, option B and D are discarded. Among options A and C, option C supports the alternative hypothesis by correctly rejecting null hypothesis, when it is false.
c. Increasing sample size, decreasing random error, increasing alpha are all suitable ways to increase the power of a test. All are correct.
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