Math 315 Biostatistics - DOC

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```							Math 315 Biostatistics         Test 2                 100 points     Fall 2006

This is a take-home, open-book, open-notes test. You may not consult with other people.
The test is due on Wednesday, Nov. 15.

For hypothesis tests, be sure you state the hypotheses, give the P-value of the test, and
state the conclusion. Use significance level 0.05.

Attach copies of relevant Minitab output and label them with the problem numbers.

A copy of this test will be available on the course web page so that you can copy and
paste data into Minitab if you like.

There is one problem for which none of our techniques of analysis is appropriate. For
that one, just state that this is so, and briefly explain why. This problem gets 5 points
credit. Others are 10 points except where indicated.

1. A 1989 study investigated the effect of heredity and environment on intelligence.
From adoption registers in France, researchers selected samples of adopted children
whose biological parents and adoptive parents came from either the very highest of the
very Lowest socio-economic status (SES) categories (based on years of education and
occupation.) The table below gives IQ scores from samples of size 8 from each
combination of high or low biological SES and high or low adoptive SES. Are the
differences in mean IQ scores statistically significant? Does the difference in mean
scores for those with high versus low SES biological parents depend on whether the
adoptive parents were high or low SES?

a. (3 points) What model would you propose to describe the relations among the
variables? What are the assumptions of the model?

b. Analyze the data and perform tests of hypotheses to answer the questions posed about
the differences in mean scores.

Adoptive SES                   Biological SES                  IQ test score
High                           High                            136
High                           High                            99
High                           High                            121
High                           High                            133
High                           High                            125
High                           High                            131
High                           High                            103
High                           High                            117
High                           Low                             94
High                           Low                             99
2

High                           Low                            125
High                           Low                            111
High                           Low                            93
High                           Low                            94
High                           Low                            125
High                           Low                            91
Low                            High                           98
Low                            High                           99
Low                            High                           91
Low                            High                           124
Low                            High                           100
Low                            High                           116
Low                            High                           113
Low                            High                           119
Low                            Low                            92
Low                            Low                            98
Low                            Low                            83
Low                            Low                            68
Low                            Low                            76
Low                            Low                            115
Low                            Low                            86
Low                            Low                            116

2. Previous studies suggest that vegetarians may not receive enough zinc in their diets.
As the zinc requirement is particularly important during pregnancy, researchers
conducted a study to determine whether vegetarian pregnant women are at greater risk
from Low zinc levels than are non-vegetarian pregnant women. Twenty-three women
were monitored: twelve vegetarians who were pregnant, six non-vegetarians who were
pregnant, and five vegetarians who were not pregnant. None of these women were
smokers, and none of the non-pregnant women were taking oral contraceptives. The zinc
status in each woman was measured by zinc content in the blood, urine, and hair. The
table on the next page presents the zinc levels in the hair.

a. Is there evidence that mean zinc levels are different among these three populations?
Carry out a test of hypotheses.

b. (5 points) Carry out Fisher’s and Tukey’s multiple comparisons. Do they agree?
Explain the difference between “family error rate” and “individual error rate.”
3

Pregnant non-vegetarians        Pregnant vegetarians            Non-pregnant vegetarians
185                             171                             210
189                             174                             139
187                             202                             172
181                             171                             198
150                             207                             177
176                             125
189
179
163
174
184
186

3. The table below is based on data from a small set of married women in a much larger
sample, who were identified as being 60 years old or older and who answered survey
questions about whether they were sexually active and whether they drank coffee.
Sexually active? Yes           No
Coffee drinker            15                             25
Not coffee drinker        115                            70

a. Do the data provide evidence that sexual activity and coffee drinking are associated?
Conduct a test of hypotheses.

b. (3 points) Could you use this data to conclude that drinking coffee affects sexual
activity? Explain.

c. (5 points) Calculate and interpret the odds ratio for sexual activity for coffee drinkers
compared to non-coffee drinkers.

4. The Pique Technique was developed because a target for solicitation is more likely to
comply if mindless refusal is disrupted by a strange or unusual request. Researchers had
young people ask 144 targets for money. The targets were asked either for a standard
amount—a quarter—or an unusual amount—17 cents. Each group contained 72 targets.
Of those asked for 17 cents, 43.1% responded, compared to 30.6% of those asked for a
quarter. Does this provide significant evidence that the Pique Technique is more
effective?
4

5. Three diets for hamsters were tested for differences in weight gain after a specified
period of time. Six inbred laboratory lines were used to investigate the responses of
different genotypes to the various diets. The lines were blocked and diets assigned
randomly. The units are grams of increase.

Diet I                  Diet II                 Diet III
Inbred lines       A    18                      14                      15
B    16                      12                      14
C    17                      16                      12
D    19                      15                      14
E    12                      10                      12
F    13                      11                      9

a. Are there significant differences among the diets in their ability to facilitate weight
gain?

b. (3 points) Was blocking important to this analysis? Explain.

6. One hundred twenty-six pairs of brothers, one member of each pair overweight and
the other of normal weight, were examined for presence of varicose veins. The data is
tabulated below. Test the hypothesis that there is no relationship between being
overweight and developing varicose veins.

Overweight
With varicose veins        Without varicose
veins
Normal weight     With varicose veins                     19                     6

Without varicose veins                  15                       86

7. A first grade teacher has an unusually large number of left-handed children in her
class this year, and this seems a good time to test whether boys and girls are equally
likely to be left-handed. The table below shows the data for her class. Are handedness
and gender independent?
Left-handed Right-handed
Boys                4               12
Girls               2               13
5

8. Researchers wished to determine if sodium citrate ingestion would improve cycling
performance and facilitate favorable metabolic conditions during the cycling ride.
Subjects were eight trained male competitive cyclists whose mean age was 25.4 years.
Each participant completed a 30-km cycling time trial under two conditions following
ingestion of sodium citrate and following ingestion of a placebo. The table gives partial
pressures of oxygen (PO2) for each subject, for each treatment, at the end of a 30-km ride.
Is there significant evidence that sodium citrate affects PO2?

Subject Treatment (1 = sodium citrate, 2 = placebo) PO2
1                         1                        56
1                         2                        55
2                         1                        76
2                         2                        46
3                         1                        56
3                         2                        65
4                         1                        62
4                         2                        72
5                         1                        50
5                         2                        67
6                         1                        53
6                         2                        57
7                         1                        65
7                         2                        57
8                         1                        51
8                         2                        49

9. (6 points) An epidemiologist wishes to test whether the proportion of adults living in a
large metropolitan area that have subtype ay hepatitis B virus is greater than 0.20. What
sample size would be required to have probability .90 of rejecting the null hypothesis
when the true proportion is 0.23 or more?

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