STAT 305 – Assignment #7 (90 pts. Due Monday, April 7th)
For each problem on this assignment be sure to show/discuss all steps in the
hypothesis testing process. Be sure to state all conclusions in the context of
research question, i.e. no “Rejecting Ho’s”.
1 – Arm Lengths of Sea Stars (Linckia laevigata)
As part of a benthic community survey of Lady Elliot Island,
16 sea stars were collected and their longest arm was
measured to nearest tenth of a centimeter. The lengths
below were obtained from this sample.
10.3 11.0 10.5 10.0 11.3 14.5 13.0 12.1
12.1 9.4 11.3 12.0 11.5 9.3 10.1 7.6
a) Is there evidence that mean maximum arm length is
different from 12 cm? (6 pts.)
b) Find a 95% CI for the mean maximum arm length of sea stars in the benthic zone of
Lady Elliot Island. Interpret this interval. (3 pts.)
c) Discuss the relationship between the confidence interval from part (b) and the
hypothesis test you conducted in part (a). (2 pts.)
2 – Maine Mercury Study
Data File: Maine Mercury Study
a) The U.S. Food and Drug Administration has determined that samples with more than
1.0 ppm mercury are above the safety limit. Maine uses .43 ppm, to be high enough to
consider taking action (e.g., issuing a health advisory, considering methods of clean-up,
etc.). As indicated by the data collected here, are mercury levels high enough to be of
concern in Maine? To answer this question, determine whether the “average” mercury
level found in fish in Maine lakes exceeds the .43 ppm cutoff. Given that Hg levels are
considerably right skewed you should consider looking at the Hg levels in the log scale
(e.g. Morgan Creek example in class). Summarize your findings. (6 pts.)
b) Construct and interpret a confidence interval for the typical mercury level found in
fish sampled from Maine lakes. You should do this by finding the confidence interval in
the log scale and back-transforming the confidence limits to the original scale. Interpret
the final interval for the researchers. (4 pts.)
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3 – Serum IgG for Patients with Linear Schleroderma
In a study of linear scleroderma, serum IgG levels were reported for nine
patients with inactive disease and 30 patients with active disease. The resulting
data are presented below:
Patients with
inactive disease:
Patients with
active disease:
680
980
1025
950
840
1250
950
1250
930
1220
800
1250
1140
1150
880
1400
2900
1300
1400
1950
1600
1430
1100
1200
1300
1000
1850
1475
1100
930
740
1550
1700
1250
660
1250
1070
820
1150
Research Question: Is there evidence to suggest that patients with active linear
scleroderma have a higher mean serum IgG level than patients with inactive?
Use JMP to analyze these data. You can enter these data in JMP yourself, one
column for disease status (Active or Inactive) and one for the Serum IgG
levels. Be sure to check assumptions and perform your analysis accordingly.
a) Perform a hypothesis test answer the question of interest and summarize your
findings. (6 pts.)
b) Find and report the 95% CI for the difference in the population means from
the JMP output. Discuss this interval in practical terms. (3 pts.)
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4 – Comparisons of the Mean Infant Birth Weight for Different
Populations of Mothers Data File: LowBirth.JMP
In this problem you will use comparative methods to compare the actual mean
birth weights of different populations of mothers based upon the presence or
absence of a potential; risk factor. The results of your comparisons will be
contained in the table below. For each situation be sure to check assumptions and
briefly summarize your findings in that regard.
Use appropriate statistical methods to make comparisons of mean birth weight
across the two populations defined by the variables below:





Prev? – did mother have history of premature labor (None or History)
Hyper – did mother have a hypertension during pregnancy (None or HT)
Smoke – did mother smoke during pregnancy (Cig or No Cig)  In notes!
Uterine – did mother have uterine irritability during preg. (Irritation or
None)
Minority – is mother a racial minority (Nonwhite or White)
a) Use both hypothesis tests and confidence intervals to compare the mean birth
weights in grams (i.e. Birth Weight (g)) of the infants born to the two populations
defined by the factors above. To organize your results enter them into the table
on the following page. For the p-value and CI columns you will need to enter
the p-value from the appropriate test for comparing the two population means
for each factor and the confidence interval for the difference in those population
means, thus for each factor you will only have one p-value and confidence
interval. Write the confidence intervals without minus signs, putting the smaller
number 1st. Report the sample size, sample mean, and sample standard
deviation (SD) for each level of the factor. (20 pts.)
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Factor
Previous History?
History
None
Hypertension
HT
None
Uterine Irritation
Irritation
None
Minority
Non-white
White
Smoking Status
Smoker
Non-smoker
Sample
Size (n)
Sample
Mean
SD
Done
73
113
in
2762.30
3045.66
the
657.85
755.80
p-value
(two-tailed)
notes!
.0094
CI for Difference in
Population Means
(𝜇𝑁𝑜𝑅𝑖𝑠𝑘 − 𝜇𝑅𝑖𝑠𝑘 )
(70.30 g, 496.41 g)
b) Briefly comment on the assumptions required for the analyses you conducted in
completing the table. Are the assumptions satisfied for each factor? (3 pts.)
c) Summarize your findings from part (a) in a clearly written paragraph, citing p-values
and confidence intervals as needed. (10 pts.)
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5 – Jaw Lengths of Siganus fuscescens (Happy Moments fish)
The siganus fuscescens or “happy moments” is a common venomous fish in
Moreton Bay. The following data are the lengths (in mm) of a sample of these
fish that are measured in two ways: from the jaw to the base of the fish and from
the jaw to the tip of the caudal fin.
Paired Difference (d)
Base Caudal d = Caudal – Base
90.0 104.0
101.1 111.0
112.9 125.5
100.3 113.2
114.4 134.4
99.3 114.5
100.5 115.2
100.8 116.8
106.4 120.0
103.8 120.0
Enter these data into JMP with one column for the Base measurement and one
column for the Caudal measurement.
a) Is there evidence that the mean caudal fin measurement is over 10 mm larger
than the mean base measurement when measured on the same fish? Conduct a
hypothesis to answer this question. (6 pts.)
b) Find a 95% confidence interval for the mean difference in these measurements taken
on the same fish. Does this interval agree with your findings from part (a)? (3 pts.)
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6 - Middle Ear Effusion in Breast-Fed and Bottle-Fed Infants
A common symptom of otitus media in young children in the prolonged
presence of fluid in the middle ear, known a middle-ear effusion. The presence
of fluid may result in termporary hearing loss and interfere with normal learning
skills in the first two years of life. One hypothesis is that babies who are breastfed for at least 1 month build up some immunity against the effects of the disease
and have less prolonged effusion than do bottle-fed babies. A small study of 24
pairs of babies is set up, where the babies are matched on a one-to-one basis
according to age, sex, socioeconomic status, and type of medications taken. One
member of the matched pair is a breast-fed baby, and other member is a bottle
fed baby. The outcome variable is the duration of middle-ear effusion after the
first episode of otitus media. The results are shown below.
Pair
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Duration of effusion in
breast-fed baby
20
11
3
24
7
28
58
39
17
17
12
52
14
12
30
7
15
65
10
7
19
34
25
Duration of effusion in
bottle-fed baby
18
35
7
182
6
33
223
57
76
186
29
39
15
21
28
8
27
77
12
8
16
28
20
Paired Difference
d=
Research Question: Do these data provide evidence that breast-fed babies have shorter
durations of effusion when compared to bottle-fed babies that are the same age, sex,
socioeconomic status, and on the same medications?
Enter these data into JMP, one column for breast-fed and one column for bottle-fed
babies, and conduct the appropriate analysis.
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a) Conduct a paired t-test to answer the research question and provide a confidence
interval for the mean difference in the ear effusion times. Discuss your findings
in practical terms the researchers would understand. (6 pts.)
b) Do you think the use of the paired t-test is appropriate for these data?
Explain why or why not. (2 pts.)
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