Normal Model - STAT E-50 Introduction to Statistics The...

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STAT E-50 - 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 Lead-Related Industry,” American Journal of Epidemiology 155 (1982). -30 -20 -10 0 10 20 30 40 50 60 0 5 10 minus 30 Frequency a) Construct the histogram, using classes of 10 - 20, 20 - 30, etc: Page 1 0 10 20 30 40 50 60 70 80 90 0 5 10 Frequency lead level 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?
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0 1 2 3 4 5 6 7 8 9 10 0 5 10 div by 15 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? 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? Page 2
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Page 3 3. Here are the descriptive statistics for the original data and the rescaled 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: div by 15 Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum div by 15 33 2.123 0.167 0.960 0.667 1.367 2.267 2.667 4.867 a) Which results changed when the data was rescaled? By how much? b) Which results did not change?
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Page 4 4. Here are the results when the data was shifted by subtracting the mean, and when the data was rescaled by dividing by the standard deviation:
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