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2.38. For each pair of twins, compute the following for the lumbar spine: A = BMD for the heavier-smoking twin − BMD for the lighter-smoking twin = x1 − x2 B = mean BMD for the twinship = (x1 + x2)/2 C = 100% × (A/B) Derive appropriate descriptive statistics for C over the entire study population.

2.38. For each pair of twins, compute the following for the lumbar spine: A = BMD for the heavier-smoking twin − BMD for the lighter-smoking twin = x1 − x2 B = mean BMD for the twinship = (x1 + x2)/2 C = 100% × (A/B) Derive appropriate descriptive statistics for C over the entire study population.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 6E
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  • Endocrinology

In Section 2.10, we described Data Set BONEDEN.DAT concerning the effect of tobacco use on BMD.

Note: 2.38-2.40 Involve computing a new variable C.  Compute C using the formula given and then use STATA to produce the output requested.

 

2.38. For each pair of twins, compute the following for the lumbar spine:

A = BMD for the heavier-smoking twin − BMD for the lighter-smoking twin = x1 − x2

B = mean BMD for the twinship = (x1 + x2)/2

C = 100% × (A/B)

Derive appropriate descriptive statistics for C over the entire study population.

2.39. Suppose we group the twin pairs according to the difference in tobacco use expressed in 10 pack-year groups (0–9.9 pack-years/10–19.9 pack-years/20–29.9 pack-years/30–39.9 pack-years/40+ pack-years). Compute appropriate descriptive statistics, and provide a scatterplot for C grouped by the difference in tobacco use in pack-years

2.40. What impression do you have of the relationship between BMD and tobacco use based on Problem 2.39?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 BONEDEN. DOC Variable ID Age zyg ht1 wt1 teal cof1 alc1 cur1 men1 pyr1 ls1 fn1 fs1 ht2 wt2 tea2 cof2 alc2 cur2 men2 BONEDEN.doc pyr2 ls2 fn2 fs2 SUB Twin 1 Twin 2 Column 2-8 9-11 12-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-55 56-61 62-67 68-73 74-78 79-83 84-88 89-93 94-98 99-103 104-108 109-114 115-120 121-126 127-132 Code Age (yrs) 1=mz_2=dz Height (cm) Weight (kg) Tea (cups/week) Coffee Alcohol Current Smoking (cigarretes/day) (cups/week) (drinks/week) Menopause Status (1=pre/2=post/3=unknown hysterectomy) Pack-years smoking Lumbar spine (g/cm**2) Femoral neck (g/cm**2) Femoral shaft (g/cm**2) Height (cm) Weight (kg) Tea (cups/week) Coffee (cups/week) Alcohol Current Smoking (cigarretes/day) Menopause Status (1=pre/2=post/3=unknown hysterectomy) Pack-years smoking (drinks/week) Lumbar spine (g/cm**2) Femoral neck (g/cm**2) Femoral shaft (g/cm**2)
Transcribed Image Text:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 BONEDEN. DOC Variable ID Age zyg ht1 wt1 teal cof1 alc1 cur1 men1 pyr1 ls1 fn1 fs1 ht2 wt2 tea2 cof2 alc2 cur2 men2 BONEDEN.doc pyr2 ls2 fn2 fs2 SUB Twin 1 Twin 2 Column 2-8 9-11 12-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-55 56-61 62-67 68-73 74-78 79-83 84-88 89-93 94-98 99-103 104-108 109-114 115-120 121-126 127-132 Code Age (yrs) 1=mz_2=dz Height (cm) Weight (kg) Tea (cups/week) Coffee Alcohol Current Smoking (cigarretes/day) (cups/week) (drinks/week) Menopause Status (1=pre/2=post/3=unknown hysterectomy) Pack-years smoking Lumbar spine (g/cm**2) Femoral neck (g/cm**2) Femoral shaft (g/cm**2) Height (cm) Weight (kg) Tea (cups/week) Coffee (cups/week) Alcohol Current Smoking (cigarretes/day) Menopause Status (1=pre/2=post/3=unknown hysterectomy) Pack-years smoking (drinks/week) Lumbar spine (g/cm**2) Femoral neck (g/cm**2) Femoral shaft (g/cm**2)
ID 1002501 1015401 1027601 1034301 1121202 1162502 1188701 1248202 1268301 1269402 1273101 1323501 1337102 1467301 1479401 1494101 1497701 1505502 1519402 1521701 1528201 1536201 1536701 1541902 1543602 1596702 1597002 1597601 1607901 1608801 1628601 1635901 1637901 1640701 1643602 1647502 1648701 1657301 1671001 1672702 2609801 age 27 42 59 61 47 33 45 73 43 43 47 47 72 58 36 47 53 49 52 44 55 44 34 37 34 46 49 36 62 76 53 42 47 44 71 72 40 49 45 41 48 zyg 2 2 2 1 2 2 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 2 1 1 1 1 2 1 2 2 2 2 2 ht1 162 165 150 159 159 163 169 160 162 165 168 168 154 161 162 149 162 164 157 167 165 165 162 163 168 163 164 163 171 161 161 166 157 151 153 152 159 164 161 159 164 wt1 57 76 114 62 58 49 78 76 64 58 60 70 81 61 55 61 62 70 53 60 68 70 60 60 57 58 72 112 97 59 68 66 65 48 49 48 54 55 47 72 71 tea1 35 42 12 56 28 35 42 42 7 7 28 0 14 0 7 0 56 0 28 0 56 0 0 1 42 42 21 1 0 0 35 7 14 12 21 14 21 21 35 0 10 cof1 0 2 0 0 14 0 0 14 2222 28 21 28 21 7 21 14 42 0 28 28 x 28 0 7 49 42 0 0 14 0 7 7 35 7 7 0 7 56 42 7 0 14 0 alc1 1 3 0 0 0 3 1 14 8 6 7 0 0 0 2 2 9 0 1 23 2 1 0 8 0 0 9 0 0 28 0 10 2 0 1 0 0 21 5 0 0 cur1 1 5 0 0 0 1 1 8 3 0 7 0 0 0 0 3 8 1 1 22 3 0 0 3 0 4 12 0 0 28 0 15 2 0 0 0 0 22 0 0 0 men1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 1 2 1 0 1 1 2 0 0 0 1 0 1 1 1 0 2 0 1 1 1 1 NOO 2 0 0 pyr1 0 0 0 0 0 0 0 25 0.5 0 16.5 0 0 0 0 12 33.75 0 0 0 0 0 0 0 0 0 19 18 0 0 24.65 0 0 28 0 1.3 0 0 0 0 0 Is1 0.81 1.01 0.75 0.81 0.78 0.86 0.95 0.76 0.83 1.01 0.86 0.71 0.71 0.7 0.73 0.71 0.73 0.83 0.65 0.77 0.75 0.89 0.62 1.04 0.87 0.95 0.67 0.71 0.5 0.69 0.82 0.93 0.8 0.86 0.5 0.58 0.98 0.76 0.93 0.82 0.95 fn1 0.72 0.74 0.63 0.64 0.7 0.56 0.83 0.56 0.65 0.9 0.7 0.85 0.55 0.68 0.64 0.61 0.82 0.66 0.66 0.66 0.59 0.78 0.61 0.82 0.65 0.71 0.74 0.6 0.49 0.54 0.69 0.73 0.67 0.6 0.47 0.42 0.69 0.65 0.57 0.67 0.81 fs1 1 0.99 1.05 1.12 1.14 1.13 1.16 1.05 1.07 1.3 1.24 1.21 0.93 1.18 1.09 1.09 1.13 1.01 0.98 1.1 1.14 1.02 1.23 1.24 1.01 1.12 1.14 1.12 1.15 0.81 1.11 1.14 1.22 1.05 0.89 0.7 1.11 1.42 1.06 1.06 1.25 | | ht2 160 159 156 162 150 158 169 161 162 168 163 167 160 160 163 154 162 165 160 167 165 165 170 163 162 157 164 167 166 155 161 165 165 153 154 155 161 164 165 164 158 wt2 56 72 54 58 58 54 84 76 60 62 53 65 80 73 54 94 55 67 55 43 71 58 72 50 58 51 68 84 56 55 60 60 62 52 43 50 59 52 60 53 88 tea2 42 20 7 21 91 14 21 7 14 0 0 0 0 0 0 0 14 4 14 28 0 21 0 0 0 42 0 21 28 14 35 0 7 0 91 7 14 7 14 0 0 24 cof2 21 21 28 35 0 14 42 7 7 35 68 28 0 14 35 0 21 28 0 28 28 42 21 35 0 35 12 0 56 0 99 14 28 0 7 42 21 0 42 35 0 alc2 0 1 0 0 0 0 2 14 7 35 0 0 0 0 0 0 9 9 0 13 0 16 0 7 0 0 14 2 8 0 0 14 14 0 14 0 28710 cur2 0 1 0 0 1 0 5 10 7 30 0 0 0 ONO 1 8 7 3 20 1 10 0 7 0 0 11 0 4 0 1 10 13 0 14 0 0 28 14 0 0 men2 0 0 1 1 1 0 0 1 0 2 0 0 1 1 0 2 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 2 1 1 0 1 2 0 1 pyr2 13.75 48 20.5 29.75 25 5 42 40 10 39 31 23.25 18.5 39 25.5 20 43.75 32 13.2 30 20.25 36.25 12 11.25 8 14 36.3 30 43.2 48 30 8 6 56 64.5 12.6 15.75 21 39 18.75 48 Is2 0.76 0.89 0.51 0.85 0.59 0.83 0.87 0.66 0.98 0.89 0.76 0.8 0.63 0.63 0.7 0.76 0.77 0.79 0.64 0.71 0.64 0.84 0.65 0.92 0.9 0.96 0.74 0.84 0.47 0.48 0.77 0.96 0.75 0.85 0.61 0.51 0.9 0.68 0.86 0.92 0.85 fn2 0.68 0.64 0.64 0.69 0.54 0.5 0.78 0.49 0.77 0.87 0.74 0.76 0.56 0.64 0.61 0.66 0.88 0.63 0.71 0.61 0.65 0.63 0.81 0.67 0.76 0.71 0.74 0.85 0.48 0.38 0.67 0.83 0.63 0.54 0.54 0.46 0.64 0.62 0.71 0.79 0.72 fs2 1.04 1.11 0.86 1.03 0.96 1.06 1.23 1.04 1.15 1.24 1.21 1.09 1.01 1.04 1.2 0.99 1.18 1.15 1.01 0.96 1.15 1.12 1.33 1.08 1.06 1.06 1.1 1.16 0.73 0.64 1.08 1.24 1.12 0.97 0.86 0.66 1.21 1.22 1.03 1.02 1.31
Transcribed Image Text:ID 1002501 1015401 1027601 1034301 1121202 1162502 1188701 1248202 1268301 1269402 1273101 1323501 1337102 1467301 1479401 1494101 1497701 1505502 1519402 1521701 1528201 1536201 1536701 1541902 1543602 1596702 1597002 1597601 1607901 1608801 1628601 1635901 1637901 1640701 1643602 1647502 1648701 1657301 1671001 1672702 2609801 age 27 42 59 61 47 33 45 73 43 43 47 47 72 58 36 47 53 49 52 44 55 44 34 37 34 46 49 36 62 76 53 42 47 44 71 72 40 49 45 41 48 zyg 2 2 2 1 2 2 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 2 1 1 1 1 2 1 2 2 2 2 2 ht1 162 165 150 159 159 163 169 160 162 165 168 168 154 161 162 149 162 164 157 167 165 165 162 163 168 163 164 163 171 161 161 166 157 151 153 152 159 164 161 159 164 wt1 57 76 114 62 58 49 78 76 64 58 60 70 81 61 55 61 62 70 53 60 68 70 60 60 57 58 72 112 97 59 68 66 65 48 49 48 54 55 47 72 71 tea1 35 42 12 56 28 35 42 42 7 7 28 0 14 0 7 0 56 0 28 0 56 0 0 1 42 42 21 1 0 0 35 7 14 12 21 14 21 21 35 0 10 cof1 0 2 0 0 14 0 0 14 2222 28 21 28 21 7 21 14 42 0 28 28 x 28 0 7 49 42 0 0 14 0 7 7 35 7 7 0 7 56 42 7 0 14 0 alc1 1 3 0 0 0 3 1 14 8 6 7 0 0 0 2 2 9 0 1 23 2 1 0 8 0 0 9 0 0 28 0 10 2 0 1 0 0 21 5 0 0 cur1 1 5 0 0 0 1 1 8 3 0 7 0 0 0 0 3 8 1 1 22 3 0 0 3 0 4 12 0 0 28 0 15 2 0 0 0 0 22 0 0 0 men1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 1 2 1 0 1 1 2 0 0 0 1 0 1 1 1 0 2 0 1 1 1 1 NOO 2 0 0 pyr1 0 0 0 0 0 0 0 25 0.5 0 16.5 0 0 0 0 12 33.75 0 0 0 0 0 0 0 0 0 19 18 0 0 24.65 0 0 28 0 1.3 0 0 0 0 0 Is1 0.81 1.01 0.75 0.81 0.78 0.86 0.95 0.76 0.83 1.01 0.86 0.71 0.71 0.7 0.73 0.71 0.73 0.83 0.65 0.77 0.75 0.89 0.62 1.04 0.87 0.95 0.67 0.71 0.5 0.69 0.82 0.93 0.8 0.86 0.5 0.58 0.98 0.76 0.93 0.82 0.95 fn1 0.72 0.74 0.63 0.64 0.7 0.56 0.83 0.56 0.65 0.9 0.7 0.85 0.55 0.68 0.64 0.61 0.82 0.66 0.66 0.66 0.59 0.78 0.61 0.82 0.65 0.71 0.74 0.6 0.49 0.54 0.69 0.73 0.67 0.6 0.47 0.42 0.69 0.65 0.57 0.67 0.81 fs1 1 0.99 1.05 1.12 1.14 1.13 1.16 1.05 1.07 1.3 1.24 1.21 0.93 1.18 1.09 1.09 1.13 1.01 0.98 1.1 1.14 1.02 1.23 1.24 1.01 1.12 1.14 1.12 1.15 0.81 1.11 1.14 1.22 1.05 0.89 0.7 1.11 1.42 1.06 1.06 1.25 | | ht2 160 159 156 162 150 158 169 161 162 168 163 167 160 160 163 154 162 165 160 167 165 165 170 163 162 157 164 167 166 155 161 165 165 153 154 155 161 164 165 164 158 wt2 56 72 54 58 58 54 84 76 60 62 53 65 80 73 54 94 55 67 55 43 71 58 72 50 58 51 68 84 56 55 60 60 62 52 43 50 59 52 60 53 88 tea2 42 20 7 21 91 14 21 7 14 0 0 0 0 0 0 0 14 4 14 28 0 21 0 0 0 42 0 21 28 14 35 0 7 0 91 7 14 7 14 0 0 24 cof2 21 21 28 35 0 14 42 7 7 35 68 28 0 14 35 0 21 28 0 28 28 42 21 35 0 35 12 0 56 0 99 14 28 0 7 42 21 0 42 35 0 alc2 0 1 0 0 0 0 2 14 7 35 0 0 0 0 0 0 9 9 0 13 0 16 0 7 0 0 14 2 8 0 0 14 14 0 14 0 28710 cur2 0 1 0 0 1 0 5 10 7 30 0 0 0 ONO 1 8 7 3 20 1 10 0 7 0 0 11 0 4 0 1 10 13 0 14 0 0 28 14 0 0 men2 0 0 1 1 1 0 0 1 0 2 0 0 1 1 0 2 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 2 1 1 0 1 2 0 1 pyr2 13.75 48 20.5 29.75 25 5 42 40 10 39 31 23.25 18.5 39 25.5 20 43.75 32 13.2 30 20.25 36.25 12 11.25 8 14 36.3 30 43.2 48 30 8 6 56 64.5 12.6 15.75 21 39 18.75 48 Is2 0.76 0.89 0.51 0.85 0.59 0.83 0.87 0.66 0.98 0.89 0.76 0.8 0.63 0.63 0.7 0.76 0.77 0.79 0.64 0.71 0.64 0.84 0.65 0.92 0.9 0.96 0.74 0.84 0.47 0.48 0.77 0.96 0.75 0.85 0.61 0.51 0.9 0.68 0.86 0.92 0.85 fn2 0.68 0.64 0.64 0.69 0.54 0.5 0.78 0.49 0.77 0.87 0.74 0.76 0.56 0.64 0.61 0.66 0.88 0.63 0.71 0.61 0.65 0.63 0.81 0.67 0.76 0.71 0.74 0.85 0.48 0.38 0.67 0.83 0.63 0.54 0.54 0.46 0.64 0.62 0.71 0.79 0.72 fs2 1.04 1.11 0.86 1.03 0.96 1.06 1.23 1.04 1.15 1.24 1.21 1.09 1.01 1.04 1.2 0.99 1.18 1.15 1.01 0.96 1.15 1.12 1.33 1.08 1.06 1.06 1.1 1.16 0.73 0.64 1.08 1.24 1.12 0.97 0.86 0.66 1.21 1.22 1.03 1.02 1.31
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Scatterplot on Stata and commentary on the relation between BMD and smoking, please!

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