Question 1:
An experiment was conducted to compare the weights of the combs of roosters fed two different vitamin-supplemented diets. Twenty-eight healthy roosters were randomly divided into two groups, with one group receiving diet I and the other receiving diet II. After the study period the comb weight (in milligrams) was recorded for each rooster. The data are:
Diet I 73 130 115 144 127 126 112 76 68 101 126 49 110 123
Diet II 80 72 73 60 55 74 67 89 75 66 93 75 68 76
a) Suppose you wanted to conduct a nonparametric test to compare these data. Using α = .05, complete the following:
H0:
Ha: (two-sided):
Value of test statistic:
p-value:
Conclusion:
b) Suppose the experimenters submitted a scientific paper on their results, and received a number of suggestions from referees. One referee suggests that the underlying distributions are normally distributed, and hence that one should compare the two mean weights. Suppose you investigate comparing means assuming normality. Give the formula for the proper statistic to use, and also the p-value.
Formula for test statistic:
p-value::
Question 2:
For the population of people who suffer occasionally from migraine headaches, suppose that p = 0.60 is the proportion who get some relief from their symptoms by taking ibuprofen.
(a) Let X be the number of individuals in a simple random sample of size 50 from this population who get some relief by taking ibuprofen, and let pˆ be the sample proportion. Find the probability that the value of pˆ is in the interval (0.55, 0.65).
(b) Repeat part (a) assuming that a sample of size 200 is used instead of a sample of size 50.
Question 3:
To study the effect of pesticides on birds, a scientist randomly and equally allocates
N= 65 chicks to five diets (a control and four with a different pesticide included). After a month each chick's calcium content (mg) in 2 cm length of bone is measured resulting in the following:
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Control
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Pesticide
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1
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2
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3
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4
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Mean
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11.54
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11.00
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11.42
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11.44
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11.28
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Standard
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0.27
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0.47
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0.31
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0.42
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0.31
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Deviation
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Construct the ANOVA table (i.e. compute the between and within SS) and test if there appears to be any differences in means (use α = 0.05)
Question 4:
Below are the Intervals from primary AIDS diagnosis until death for a sample of 12 hemophiliac patients at most 40 years of age at HIV seroconversion.
ID Survival (months)
1 2
2 3
3 6
4 6
5 7
6 10
7 15
8 15
9 16
10 27
11 30
12 32
(a) Use the Kaplan-Meier (product-limit) method to estimate the survival function.
(b) Construct a survival curve based on the product-limit estimate.
(c) Estimate the median survival time
Question 5:
In this question, please use Minitab (or other software package you are familiar with) to carry out logistic regressions using the Low Birth Weight data. The data set is lowbwt.mtw (from ch18: exercise 9)
Values of infant germinal matrix hemorrhage are saved under the variable grmhem, and values of mother's toxemia status under the name tox. Using grmhem as the response, and tox as the predictor variable, fit a logistic regression model.
grmhem = 1 if infant had hemorrhage, grmhem = 0 if no hemorrhage
tox= 1 if mother had toxemia tox= 0 if no toxemia
Based on the Minitab output, complete the following:
a) Interpret the estimated coefficient for the toxemia variable (tox)
b) What are the odds of a hemorrhage for infants whose mother had toxemia?
c) What is the probability of hemorrhage for infants whose mothers had toxemia?
d) What is the odds ratio of hemorrhage for children whose mothers had toxemia relative to those mothers were not diagnosed with toxemia?
e) Using the estimates and standard errors from the output, conduct 95% confidence interval for the population odds ration in (D). Use a z critical value of 1.96.