80
Math 156–Sat: HW #6
Name:
1. On April 12, 1955, Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent
polio. In these clinical trials, 400000 children were randomly divided into two groups (200000 in
each). The subjects in Group 1 (the experimental group) were given the vaccine, while the subjects in
Group 2 (the control group) were given a placebo. Of the 200000 given the vaccine, 33 developed
polio. Of the 200000 in the control group, 115 developed polio. Test, at the 0.01 level, the claim that
the proportion of people who develop polio is lower for those who take the vaccine than for those
who do not. (10 points)
2. “Is smoking by Americans on the decline?” In November 2005, the Gallup Organization surveyed
1028 adults and found that 226 of them had smoked at least one cigarette in the past week. In 1990, a
similar survey showed that 278 of 1028 adults had smoked at least one cigarette in the previous week.
Can we say that the proportion of Americans who smoked at least one cigarette in the last week
decreased between 1990 and 2005? Test the relevant hypotheses at the 0.05 level. (10 points)
3. Urinary fluoride concentration (in parts per million) was measured for both a sample of livestock that
had been grazing in an area previously exposed to fluoride pollution and a similar sample of livestock
that had grazed in an unpolluted region. Do the data strongly indicate that the true average fluoride
concentration for livestock grazing the polluted region is larger than that for livestock grazing the
unpolluted region? Assume only that both populations have similar shape and spread. Test the
appropriate hypotheses at the 0.05 level.
Polluted:
21.3
Unpolluted: 14.2
18.7
18.3
23.0
17.2
17.1
18.4
16.8
20.0
20.9
19.7
4. A blood lead level of 70 mg/ml has been commonly accepted as safe. However, researchers have
noted that some neurophysiological symptoms of lead poisoning appear in people whose blood lead
levels are below 70 mg/ml. The article “Subclinical Neuropathy at Safe Levels of Lead Exposure”
(Archives of Environmental Health [1975]) gave the following nerve-conduction velocities for a
group of workers who were exposed to lead in the workplace but had blood lead levels below 70
mg/ml and for a group who had no exposure to lead. Use a level 0.01 test (assuming nothing but
similar shape and spread for both populations) to determine whether there is a significant difference
in mean conduction velocity between workers exposed to lead and those not exposed to lead.
Exposed
Not Exposed
46
54
46
50.5
43
46
41
45
38
44
36
42
31
41
5. According to the manufacturer of M&M’s, 13% of the plain M&M’s in a bag should be brown, 14%
should be yellow, 13% should be red, 20% should be orange, 24% should be blue and 16% should be
green. A consumer advocate tested this by counting the number of each color in a bag of plain
M&M’s. The frequencies are shown below. Test the relevant hypotheses at the 0.05 level to
determine whether or not the proportions (as stated by the Mars Candy Company) are accurate.
(10 points)
Color
Brown
Yellow
Red
Blue
Orange
Green
Frequency
61
64
54
61
96
64
6. An obstetrician wants to learn whether the amount of prenatal care and the wantedness of the
pregnancy are associated. He randomly selects 939 women who had recently given birth and asks
them to disclose whether their pregnancy was intended, unintended, or mistimed. In addition, they
were to disclose when they started receiving prenatal care, if ever. The results are in the table below.
Test, at the 0.05 level, whether amount of prenatal care and wantedness of pregnancy are
independent. (10 points)
Months Pregnant Before Prenatal Care Began
Wantedness
of Pregnancy
< 3 months
3 to 5 months
More than 5
months
(or never)
Intended
593
26
33
Unintended
60
13
10
Mistimed
169
19
16
7. An economist wants to gauge the level of satisfaction of Americans. He randomly samples 150
people 18 years old or older from four geographic locations of the U.S.: East, South, Midwest, and
West. He asks them, “Are you satisfied or dissatisfied with the way things are going in the Unites
States at this time?” The table below gives the results. Test at the 0.10 level if “satisfied or not” and
“region of the country” are independent. (10 points)
Region
Satisfaction
East
South
Midwest
West
Satisfied
77
84
93
83
Dissatisfied
73
66
57
67
8. A researcher wants to know whether the distribution of birth month is uniform (i.e. the proportion of
births for each month is the same). The following data, based on results from Vital Statistics of the
United States, 2005, Volume 1, represents the distribution of months in which 500 randomly selected
children were born. Is there reason to believe that each birth month occurs with equal frequency?
Test the relevant hypotheses at the 0.05 level. (10 points)
Month
Jan.
Feb.
March
April
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Births
40
38
41
40
42
41
45
44
44
43
39
43