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FinalExam06_solution - Part I Problem Recognition(24 marks...

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Part I - Problem Recognition (24 marks, 3 marks each) – 2 for hypotheses, 1 for test 1. A ski company in Whistler owns two ski shops, one near Whistler and one near Blackcomb. The following data were collected from both stores: Whistler shop Blackcomb shop Mean sales $328 $435 Sample std. Dev. $104 $151 Sample size 35 days 30 days The company would like to test for a difference in daily average goggle sales between the two stores H 0 : μ w − μ B = 0 H A : μ w − μ B ≠ 0 Test: t test Not equal variance 2. The state lottery office claims that the average household income of those people playing the lottery is greater than $37,000. They also know that the distribution of these households’ income is normal with a standard deviation of $5,756. To test their claim a sample of 25 households was studied. It was found that the average income in the sample was $36,243. H 0 : μ < 37,000 H A : μ > 37,000 Test: Z test 3. In random samples of 1000 people in the United States and in France, 70% of the people in the Unites States and 75% of the people in France indicated that they were positive about the future economy. Does this provide strong evidence that the people in France are more optimistic about the economy? H 0 : p F p US < 0 H A : p F p US > 0 Test: Z test 4. The distributor of the post, a regional newspaper serving North York is considering three types of dispensing racks. Management wants to know if the different racks affect sales. These racks are designated as J-1000, D, and UV-57. Management also wants to know if the placement of the racks either inside or outside supermarkets affects sales. Each of six similar stores was randomly assigned a machine and location combination, and data were collected on the number of papers sold over four days. Ho: no interaction Ha: interaction Ho: μ j-1000 = μ D = μ UV57 Ha: at least two means differ Ho: μ inside = μ outside Ha: at least two means differ Two-way ANOVA
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5. A pasta chef was experiencing difficulty in getting brands of pasta to be cooked just right. The main problem she experiences is with the speed of water absorption by the different pasta brands. Pasta with a faster rate of water absorption has a greater tendency to be overcooked. She decides to conduct an experiment in which two brands of pasta, one Canadian and one Italian, were cooked for either 4 or 8 minutes. The variable measured was the speed of water absorption in each case. The results were then recorded an analyzed. Ho: no interaction Ha: interaction Ho: μ c = μ I Ha: at least two means differ Ho: μ 4 = μ 8 Ha: at least two means differ Two-way ANOVA 6. A large milling machine produces steel rods to certain specifications. The machine is considered to be running normally if the standard deviation of the diameter of the rods is 0.15 millimeters. As line supervisor, you need to test to see whether the machine is operating normally. You take a sample of 25 rods and find that the sample standard deviation is 0.19.
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