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Unformatted text preview: STAT E50  Introduction to Statistics The Normal Model 1. Researchers have investigated lead absorption in children of parents who worked in a factory where lead is used to make batteries. Shown below are the levels of lead in the children’s blood (in μ g/dl of whole blood): 38 23 41 18 37 36 23 62 31 34 24 14 21 17 16 20 15 10 45 39 22 35 49 48 44 35 43 39 34 13 73 25 27 Source: D. Morton, et al., “Lead Absorption in Children of Employees in a LeadRelated Industry,” American Journal of Epidemiology 155 (1982). 10 20 30 40 50 60 70 80 90 5 10 lead level Frequency a) Construct the histogram, using classes of 10  20, 20  30, etc: 2302010 10 20 30 40 50 60 5 10 minus 30 Frequency 10 20 30 40 50 60 70 80 90 5 10 lead level Frequency b) What would the data look like if we shift the data by subtracting 30 from each value? What happens to center of the data? What happens to the spread? 3302010 10 20 30 40 50 60 5 10 minus 30 Frequency 10 20 30 40 50 60 70 80 90 5 10 lead level Frequency b) What would the data look like if we shift the data by subtracting 30 from each value? What happens to center of the data? The center shifts 30 units to the left; new center = old center  30 What happens to the spread? The spread is unchanged 4 1 2 3 4 5 6 7 8 9 10 5 10 div by 15 Frequency 10 20 30 40 50 60 70 80 90 5 10 lead level Frequency c) What would the data look like if we rescale the data by dividing each of the original values by 15? What happens to center of the data? What happens to the spread? 5 1 2 3 4 5 6 7 8 9 10 5 10 div by 15 Frequency 10 20 30 40 50 60 70 80 90 5 10 lead level Frequency c) What would the data look like if we rescale the data by dividing each of the original values by 15? What happens to center of the data? The center is much smaller What happens to the spread? The spread is much smaller 6 2. Here are the descriptive statistics for the original data and the shifted data: Descriptive Statistics: lead level Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum lead level 33 31.85 2.51 14.41 10.00 20.50 34.00 40.00 73.00 Descriptive Statistics: minus 30 Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum minus 30 33 1.85 2.51 14.41 20.00 9.50 4.00 10.00 43.00 a) Which results changed when the data was shifted? By how much? b) Which results did not change? 7 2. Here are the descriptive statistics for the original data and the shifted data: Descriptive Statistics: lead level Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum lead level 33 31.85 2.51 14.41 10.00 20.50 34.00 40.00 73.00 Descriptive Statistics: minus 30 Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum minus 30 33 1.85 2.51 14.41 20.00 9.50 4.00 10.00 43.00 a) Which results changed when the data was shifted? By how much?...
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 Spring '08
 WEINSTEIN
 Statistics, Normal Distribution, Standard Deviation, Mean, Descriptive statistics

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