Comprehensive Take-Home Exam STAT 210 (?? pts.)
(DUE 12/8/04)
1 – Risk Factors for Low Birth Weight
These data come from a study of infant birth weights. Two of the factors of interest to researchers are maternal smoking during pregnancy and age of the mother and the role these factors might play in the birth weight of the infant. It is believed that smoking mothers and mothers over the age of 35 are at increased risk of having an infant with low birth weight, which is a birth weight below 6 lbs.
Data from this study are contained in the file Lowbirthweight.JMP. The variables in the data file are as follows:
· Head Circum – head circumference of infant
· Length – length of infant (in.)
· Birth Weight – birth weight (lbs.)
· Gestational Age – age of infant in weeks
· Mother’s Age – age of mother (yrs.)
· Mother’s Cigarettes – number of cigarettes smoked per day during pregnancy
· Mother’s Height – height of mother (in.)
· Mother’s Pre-Preg Wt – mother’s pre-pregnancy weight (lbs.)
· Father’s Age – age of father
· Father’s Educ – father’s education level (yrs. of schooling)
· Father’s Cigarette – number of cigarettes smoked per day by father
· Father’s Height – height of father (in.)
· Over Age 35? – Is mother over the age of 35? (Yes or No)
· Smoker – Did mother smoke during pregnancy? (Yes or No)
· Low Birth Weight – Did infant have a low birth weight (< 6 lbs.)? (Yes or No)
In Parts (a) – (c) you will examine whether or not women over 35 years of age and women who smoke during pregnancy have a significantly better chance of having an infant with low birth weight.
a) Find the following conditional probabilities: (4 pts.)
P(LBW=Yes|Over 35 = Yes) P(LBW=Yes|Over 35 = No)
P(LBW=Yes|Smoker = Yes) P(LBW=Yes|Smoker=No)
b) Use the conditional probabilities from part (a) to find the Relative Risk (RR) of having an infant with low birth weight associated with both of these potential risk factors.
Give the correct interpretations of both of these RR’s. (4 pts.)
1 – Low Birth Weights (cont’d)
c) Use an appropriate inferential method to determine if these two risk factors are statistically significant, specifically test whether or not having the risk factor increases the chance of having a infant with a low birth weight. Summarize your findings including any appropriate computer output you used. (8 pts.)
In Parts (d) – (f) you will be comparing the actual birth weights of infants.
d) Construct a comparative display that shows the birth weights plotted vs. smoking status of the mother. Obtain summary statistics (mean, median, quantiles, SD, etc.) for the birth weights of infants from both groups. How do the birth weights compare on the basis of these statistics? (3 pts.)
NOTE: Parts (e) – (g) require material from Chapter 14 which we have not yet discussed, therefore I would not recommend tackling these until we have gone over this material in lecture.
e) Conduct a test to determine if smoking mothers have significantly smaller infants on average when compared to mothers who did not smoke during pregnancy. Summarize your findings. (4 pts.)
f) Construct a 95% CI for the difference in mean birth weight for infants born to smoking vs. non-smoking mothers. Interpret this interval. (3 pts.)
g) Repeat parts (d) – (f) using the age over 35 as the potential risk factor. Briefly summarize your findings. (5 pts.)
2 – WSU Student Survey Results
Two of the variables examined in a recent WSU student survey regarded smoking and drinking (alcohol) habits. Specifically, amongst students who smoke:
· How many cigarettes do they smoke per day?
and amongst students who drink alcohol
· How many drinks do they have per drinking episode?
Which has more variation the number of cigarettes smoked per day by WSU students who smoke or the number drinks per episode consumed by WSU students who regularly drink? Explain. (3 pts.)
Cigarettes per day Drinks per episode
3 – Effectiveness of a New Reading Program
A new reading program may reduce the number of elementary students who read below grade level. The company that developed this program supplied materials and teach training for a large-scale test involving nearly 8500 children in several different school districts. Statistical analysis of the results showed the percentage of students who did not attain the grade level standard was reduced from 15.9% to 15.1%. The hypothesis that the new reading program produced no improvement was rejected with a p-value of .023.
a) Explain what the p-value means in this context. (2 pts.)
b) Even though this reading method has been shown to be significantly better, why might you not recommend that your local school adopt it? Explain. (2 pts.)
4 – Salaries of Minnesota Teachers
Analysis of a sample of 288 Minnesota teachers salaries produced the following 90% confidence interval for the mean teachers salary in Minnesota.
90% CI for Mean MN Teacher Salary
($38,944 , $42,893)
Which conclusion below is correct? What’s wrong with the others? (1 pt. each)
a) If we took many random samples of MN teachers, about 9 out of 10 of them would produce this confidence interval.
b) If we took many samples of MN teachers, about 9 out of 10 of them would produce a confidence interval that would cover the true mean salary of all MN teachers.
c) About 9 out of 10 MN teachers earn between $38,944 and $42,893.
d) About 9 out of 10 of the teachers surveyed earn between $38,944 and $42,893.
e) We are 90% confident that the average teacher salary in the United States is between $38,944 and $42,893.
5 – Vaccination Rates for Children in the United States
Public health officials believe that 90% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that among the more than 13,000 children only 89.4% had been vaccinated. A statistician would reject the 90% hypothesis with a p-value of .011.
a) Explain what the p-value means in this context. (2 pts.)
b) The result is statistically significant, but is it important? Explain. (2 pts.)
6 – Number of Eggs per Duck Nest
A random sample n = 9 of duck nests in Mississippi Wildlife Refuge yielded the following data for the number eggs in the nest:
13 11 8 6 6 4 7 9 8
a) Find the sample mean (2 pts.)
b) Find the sample median (2 pts.)
c) Find the sample mode (1 pt.)
d) Find the sample variance and sample standard deviation (6 pts.)
e) Find the standard error of the mean (1 pt.)
f) Construct and interpret a 90% CI for the m = mean number of eggs per duck nest in the Mississippi Wildlife Refuge. (4 pts.)
g) Explain why you think this CI is not appropriate based upon assumptions that might be violated. (2 pts.)
7 – Body Mass Index and Anorexia Nervosa (under construction)
These data come from a study of women who are receiving treatment for anorexia nervosa. One measure of the effectiveness of the treatment is a weight gain which in the case of this analysis will be represented by change in body mass index (BMI).
Data File: Anorexia-bodymass.JMP
a) Is there evidence to suggest that for anorexic women receiving this treatment there is an increase in their mean body mass index (BMI)? (4 pts.)
b) Estimate with 95% confidence the mean change in their BMI. Interpret this interval in practical terms. (4 pts.)
c) Is there evidence to suggest that the BMI index at discharge significantly differs from the preferred BMI determined at the start of treatment? (4 pts.)
d) True or False. All women in this study were at or above the preferred BMI at the time of discharge. Explain. (2 pts.)
e) Estimate with 95% confidence the percent increase in the BMI for women receiving this treatment. Interpret this interval in practical terms. (4 pts.)