Data Analysis (Math 206) Exam 1 - Kenyon College
Data Analysis (Math 206) Exam 1
Spring 2008 – Hartlaub
Solve all of the problems below, and be careful not to spend too much time on a particular problem. The point values are in parentheses and all files mentioned are in the directory p:\data\math\hartlaub\dataanalysis. To receive maximum credit, show all of your work. Good luck and enjoy the break!Complete all of the problems below. The point values for each part are provided in parentheses. You must show your work in order to receive the maximum amount of credit. Good luck and have a great break!
1. Researchers used 7 red and 7 black playing cards to randomly assign 14 volunteer males with high blood pressure to one of two diets for 4 weeks: a fish oil diet and a regular oil diet. The reductions in diastolic blood pressure are shown in fishoil.dat. Use the SAS program fishoil.sas to answer the questions below.
a. Why might the results of this study be important, even though the volunteers do not constitute a random sample from any population? (5)
b. Are the average reductions in diastolic blood pressure significantly different for these diets? Be sure to identify your parameters, state appropriate hypotheses, and provide a statistical justification for your conclusion. (20)
c. For the regular oil diet group, identify the standard error for the average of this group. (5)
d. Would it be reasonable to test the hypothesis that [pic]= (mean drop in diastolic blood pressure) is zero against a one-sided alternative? If so, conduct the appropriate test. If not, explain why not. (10)
e. What is the typical reduction in blood pressure that is expected from a fish oil diet for individuals like these men? Provide and interpret a 95% confidence interval. (15)
2. Researchers took independent random samples from two populations of policeman and measured the level of lead concentration in their blood. The sample of 126 police officers subjected to constant inhalation of automobile exhaust fumes in downtown Cairo had an average blood level concentration of 29.2 [pic] and a standard deviation of 7.5[pic]. A control sample of 50 policemen from the Cairo suburb of Abbasia, with no history of exposure, had an average blood level concentration of 18.2[pic] and a standard deviation of 5.8[pic]. Is there convincing evidence of a difference in the population averages? Explain. (20)
3. A sunscreen sunlight protection factor (SPF) of 5 means that a person who can tolerate Y minutes of sunlight without sunscreen can tolerate 5Y minutes of sunlight with sunscreen. The data in SPF.dat are the times in minutes that 13 patients could tolerate the sun (a) before receiving the treatment and (b) after receiving a particular sunscreen treatment. Use the SAS program SPF.sas to answer the questions below.
a. Estimate the sunlight protection factor. (5)
b. Provide a confidence interval for the sunlight protection factor. (10)
c. Is the sunlight protection factor significantly different from the hypothesized value? Be sure to state your hypotheses, test statistic, p-value, and conclusion. (15)
4. In comparing 10 groups a researcher notices that [pic] is the largest and [pic] is the smallest, and then tests the hypothesis that[pic]. Why should a multiple comparison procedure be used even though there is only one comparison being made? (10)
5. 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 nonvegetarian pregnant women. Twenty-three women were monitored: twelve vegetarians (PV) who were pregnant, six nonvegetarians (PN) who were pregnant, and five vegetarians who were not pregnant (NV). The zinc status in each woman was measured by zinc content in the blood, urine, and hair. Zinc.dat contains the zinc levels in the hair. Use the SAS program Zinc.sas to answer the questions below.
a. Identify the appropriate model for this observational study. (5)
b. Are the mean zinc levels obtained from hair for these groups of women significantly different? Explain. (15)
c. Does a complete analysis of your model in part (a) provide any evidence that pregnant vegetarians tend to have lower zinc levels than pregnant nonvegetarians? Explain. (10)
6. Eric Newman designed an experiment to study the effect of magnetic fields on data stored on removable PC disks. When the diskettes are exposed to a magnetic field with enough strength, the coating on the surface of the diskette loses its magnetism and any data stored on that part of the diskette is lost. He stored the same data on several types of disks, subjected the disks to a magnetic field, and then measured data errors. The data appear in disk.dat. The disks were of two sizes (3.5 and 5.25 inches) and three different brands (classified as expensive, middle, or cheap). The response variable is the count of errors, converted to a standard scale. The data file also includes the random order in which the disks were recorded and tested. The main objective of the experiment was to determine if more expensive disks are more resistant to data loss. Use the SAS program disk.sas to answer the questions below.
a. Identify the appropriate model for this experiment. (5)
b. Should profile plots be used to check for interaction? If so, explain if the profile plots provide evidence of interaction. If not, explain why not. (10)
c. Provide a complete analysis, including appropriate tests, and state your conclusions in the context of this experiment. Be sure to check your assumptions. Which effect is more important? (25)
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