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TABLE E2.18

LDL (mmol/L)

Subject Cornflakes Oat Bran1 4.61 3.842 6.42 5.573 5.40 5.854 4.54 4.805 3.98 3.686 3.82 2.967 5.01 4.418 4.34 3.729 3.80 3.49

10 4.56 3.8411 5.35 5.2612 3.89 3.7313 2.25 1.8414 4.24 4.14

2.19 An experiment was conducted at the University of California–Berkeleyto study the e¤ect of psychological environment on the anatomy of the

brain. A group of 19 rats was randomly divided into two groups. Twelveanimals in the treatment group lived together in a large cage furnishedwith playthings that were changed daily; animals in the control grouplived in isolation with no toys. After a month, the experimental animalswere killed and dissected. Table E2.19 gives the cortex weights (thethinking part of the brain) in milligrams. Calculate separately for eachgroup the mean x , variance s

2, and standard deviation s of the cortexweight.

TABLE E2.19

Treatment Control

707 696 669740 712 650745 708 651652 749 627649 690 656676 642699 698

2.20 Ozone levels around Los Angeles have been measured as high as 220parts per billion (ppb). Concentrations this high can cause the eyes toburn and are a hazard to both plant and animal life. But what about

98 DESCRIPTIVE METHODS FOR CONTINUOUS DATA

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other cities? The following are data (ppb) on the ozone level obtained ina forested area near Seattle, Washington:

160 165 170 172 161176 163 196 162 160162 185 167 180 168163 161 167 173 162169 164 179 163 178

(a) Calculate x , s2, and s; compare the mean to that of Los Angeles.

(b) Calculate the coe‰cient of variation.

2.21 The systolic blood pressures (in mmHg) of 12 women between the agesof 20 and 35 were measured before and after administration of a newlydeveloped oral contraceptive (Table E2.21). Focus on the column of di¤erences in the table; calculate the mean x , variance s

2, and standarddeviation s.

TABLE E2.21

Subject Before AfterAfter–BeforeDi¤erence, d i 

1 122 127 52 126 128 23 132 140 84 120 119 À15 142 145 36 130 130 07 142 148 68 137 135 À29 128 129 1

10 132 137 511 128 128 012 129 133 4

2.22 A group of 12 hemophiliacs, all under 41 years of age at the time of HIVseroconversion, were followed from primary AIDS diagnosis until death(ideally, we should take as a starting point the time at which a personcontracts AIDS rather than the time at which the patient is diagnosed,but this information is unavailable). Survival times (in months) fromdiagnosis until death of these hemophiliacs were: 2, 3, 6, 6, 7, 10, 15, 15,16, 27, 30, and 32. Calculate the mean, geometric mean, and median.

2.23 Suppose that we are interested in studying patients with systemic cancerwho subsequently develop a brain metastasis; our ultimate goal is toprolong their lives by controlling the disease. A sample of 23 such

EXERCISES 99