ch_10_Notes

# 2 can we conclude at a 005 level of significance that

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gallon performance of J cars? (2) Can we conclude at a 0.05 level of significance that the miles per gallon performance of M-cars is greater than the miles per gallon performance of J cars by 2 mpg ? 10

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Inference about the difference of mean in two populations for Matched samples : Independent samples vs. matched samples : a)Independent Sample Design: A simple random sample of workers is selected and each worker in the sample uses method 1. A second independent simple random sample of workers is selected and each worker in this sample uses method 2. The test of the difference between means is based on the procedures in Section 10.2. b)Matched Sample Design: One simple random sample of workers is selected. Each worker first uses one method and then uses the other method. The order of the two methods is assigned randomly to the workers. Each worker provides a pair of data values. Remarks: The matched sample design is referred to as blocking design . It leads to a smaller sampling error than the independent sample-design because the variation between sampled items is eliminated. 11
Example: Express Deliveries A Chicago based firm has documents that must be quickly distributed to district offices throughout the United States. The firm must decide between UPX (United Parcel Express) and INTEX (International Express). Suppose that Matched Experiment is used. (Matched Experiment: The firm decides to send two reports each to the 10 randomly chosen offices, one of which is delivered by UPX and the other by INTEX.) Do the data indicate a difference between mean delivery times for UPX and INTEX at α=0.05? Also find its 95% confidence interval. Assume the population is normally distributed. Delivery Time (Hours) District Office UPX INTEX Difference Seattle 32 25 Los Angeles 30 24 Boston 19 15 Cleveland 16 15 New York 15 13 Houston 18 15 Atlanta 14 15 St. Louis 10 8 Milwaukee 7 9 Denver 16 11 Let μ d be the mean of the difference values for the two delivery services for the population of all district offices. 12

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Example: Arnold Palmer and Tiger Woods are two of the best golfers to ever play the game. The question was raised as to how these two golfers would have compared if both were playing at the top of their game. The following sample data show the results of 18- hole scores during a PGA tournament competition. Palmer’s scores are from his 1960 season, while Wood’s scores are from his 1999 season ( Golf Magazine , February 2000). Palmer, 1960 Woods, 1999 1 x = 69.95 2 x = 69.56 n 1 = 112 n 2 = 84 Use the sample results to test the hypothesis of no difference between the population mean 18-hole scores for the two golfers.
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