Section7.78.pdf

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Department
Statistical Sciences
Course
Statistical Sciences 2035
Professor
Steve Kopp
Semester
Winter

Description
Comparing Two Population: Paired Differences (section 7.7) Things start off as a 2-sample problem: x1= sample data from population1 x = sample data from population 2 2 In a paired differences situation, subjects/people in an experiment (or sample) are matched in pairs • that is, you use the same group of subjects/people in both samples (thus, n1= n 2 n) Calculate the difference in each matched pair: d = x − x 1 2 Then calculate the mean and std dev of d Σd Σ(d −d) d = sd= n n 1 You have now taken a 2-sample problem and reduced it to a 1-sample problem You can calculate CI’s for µ = µ − µ using d 1 2 1-sample methods. A 100(1 − α)% CI for µ d µ −1µ is2 (n−1)s d tα /2 d ± n Example 7.13 A researcher asked 16 subjects to perform several tasks before and after 24 hours of sleep deprivation. One task involved the subjects lifting weights until muscle failure. The table below gives the count of the number of bench presses done before and after 24 hours of sleep deprivation. Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Pre 19 11 9 51 60 23 20 32 16 11 26 45 26 10 8 15 (1 ) Post 19 10 8 51 58 21 17 28 16 9 22 40 20 7 6 11 (2 ) d = 0 1 1 0 2 2 3 4 0 2 4 5 6 3 2 4 x1− x2 Calculate a 90% confidence interval for the difference in the mean number of bench presses before and after sleep deprivation. Solution to 7.13 Example 7.14 In order to measure the effect of a storewide sales campaign on non-sale items, the research director of a national supermarket chain took a random sample of 13 pairs of stores that were matched according to average weekly sales volume. One store of each pair was exposed to the sales campaign and the other store was not. The following is the weekly sales of the non-sale items (in $000): Store With Without Store With Without Sales Sales d Sales Sales d Campaign Campaign Campaign Campaign 1 67.2 65.3 1.9 7 57.3 52.4 4.9 2 59.4 54.7 4.7 8 75.2 69.9 5.3 3 80.1 81.3 −1.2 9 94.7 89.0 5.7 4 47.6 39.8 7.8 10 64.3 58.4 5.9 5 97.8 92.5 5.3 11 31.7 33.0 −1.3 6 38.4 37.9 0.5 12 49.3 41.7 7.6 13 54.0 53.6 0.4 Calculate a 95% confidence interval for the difference in average sales betwee
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