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Statistics Homework Solutions 159

Statistics Homework Solutions 159 - 159 SECTION 6.13...

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SECTION 6.13 159 3. increase. If the level increases, the probability of rejecting H 0 increases, so in particular, the probability of rejecting H 0 when it is false increases. 5. (a) H 0 : μ 50 000 versus H 1 : μ 50 000. H 1 is true, since the true value of μ is 49,500. (b) The level is the probability of rejecting H 0 when it is true. Under H 0 , X is approximately normally distributed with mean 50,000 and standard deviation σ X 5000 100 500. The probability of rejecting H 0 is P X 49 400 . Under H 0 , the z -score of 49,400 is z 49 400 50 000 500 1 20. The level of the test is the area under the normal curve to the left of z 1 20. Therefore the level is 0.1151. The power is the probability of rejecting H 0 when μ 49 500. X is approximately normally distributed with mean 49,500 and standard deviation σ X 5000 100 500. The probability of rejecting H 0 is P X 49 400 . The z -score of 49,400 is z 49 400 49 500 500 0 20. The power of the test is thus the area under the normal curve to the left of z 0 20. Therefore the power is 0.4207. (c) Since the alternate hypothesis is of the form μ μ 0 , the 5% rejection region will be the region
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