1. Stating the hypotheses. In each of the following situations a significance te
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Question
1. Stating the hypotheses. In each of the following situations a significance test for a population mean µ is called for. Identify the null hypothesis H0 and the alternative hypothesis Ha in each case. Make sure to use proper notation! (e.g. H0 : µ = µ0).
(a) A company produces an item that is supposed to have a six inch hole punched in the center. A quality control inspector is concerned that the machine which punches the hole is “out-of-control”. In an effort to test this, the inspector is going to gather a random sample of items punched by the machine and measure the diameter of the holes.
(b) The managers at Hunter Chemical Company claim that their major product contains, on average, 4.0 fluid ounces of caustic material per gallon. They further state that the distribution of caustic material is normal with a standard deviation of 1.3 fluid ounces. If there is too much caustic material, the product will be dangerous. A government inspector believes that the product is indeed dangerous. She randomly selects a sample of 100, gallon-size containers of the product and finds that their mean weight of caustic materials is 4.5 fluid ounces per gallon.
(c) The University bookstore tells prospective students that the average cost of its textbooks is $52 with a standard deviation of $4.50. A group of statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students select a random sample of size 100. Assume that the mean from their random sample is $52.80.
(d) The FMA Company has designed a new type of 16 lb bowling ball. They believe that this ball would improve a person’s bowling score. The company knows that the average man who bowls in a scratch league with the company’s old ball has a bowling score of 155. The variance of these scores is 100. The company asks a random sample of 100 men bowling in scratch leagues to bowl for five weeks with their new ball. The mean bowling score for these men with the new ball is 170. There is no reason to believe the variance is any different with the new ball.
(e) A school principal wants to test if it is true that high school juniors use the computer an average 3.2 hours a day. He selects a random sample of 50 high school juniors and finds out that they use the computer an average of 3.1 hours a day.
Explanation / Answer
a.
H0 = the machine which punches the hole is “out-of-control”
H1 = the machine which punches the hole is in control”
b.
µ0 = 4.0 fluid ounces of caustic material per gallon
µ1 > 4.0 fluid ounces of caustic material per gallo
C.
µ0 = the average cost of its textbooks is $52
µ1 > the average cost of its textbooks is $52
E.
µ0 = the computer an average of 3.1 hours a day.
µ1 = the computer an average IS NOT3.1 hours a day.
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