FINAL EXAM ~ Take-Home Portion ( 55 pts.)
1. Election Poll
Five candidates have just entered the race for mayor of a large city. To determine whether any of the candidates has an early lead in popularity, a poll is conducted. Some 2,000 voters are asked to indicate the candidate they prefer. A summary of their responses is shown in the table below.
CANDIDATE
Frequency / 385 / 493 / 628 / 235 / 259
a) Do the data provide sufficient evidence to indicate a preference for at least one of the five candidates? State your final conclusion in words. (5 pts.)
b) Candidate III, who clearly has the early advantage based on our sample, would like a range of values that is very likely to reflect the actual proportion of voters who prefer her. Construct such an interval. (4 pts.)
2. Tattoos and Hepatitis C
A study from the University of Texas Southwestern Medical Center examined whether the risk of hepatitis C was related to whether people had tattoos and to where they got their tattoos. Hepatitis C causes about 10,000 deaths each year in the United States, but often lies undetected for years after infection.
To investigate the potential relationship between tattoo status and hepatitis C status 626 patients being treated at the medical center for non-blood-related disorders were sampled and were classified according to both their tattoo status and their hepatitis C status. The results are shown below.
Hepatitis StatusTattoo Status / Hepatitis C / No Hepatitis C / Row Total
Tattoo, parlor / 17 / 35 / 52
Tattoo, elsewhere / 8 / 53 / 61
None / 22 / 491 / 513
Column Total / 47 / 579 / n = 626
a) Calculate the conditional probabilities of having Hepatitis C given their tattoo status.
Discuss. (3 pts.)
b) Is this a test of independence or homogeneity? Explain. (1 pt.)
c) Perform the appropriate test and summarize your findings. (5 pts.)
d) What violation of chi-square test assumptions is violated here? (1 pt.)
The table below combines the two tattoo categories into one. Use this table to answer questions (e) & (f).
Hepatitis C StatusTattoo Status / Hepatitis C / No Hepatitis C / Row Total
Tattoo / 25 / 88 / 113
None / 22 / 491 / 513
Column Total / 47 / 579 / n = 626
e) What is the relative risk for hepatitis C associated with having a tattoo? Interpret.
(2 pts.)
f) Perform an appropriate test of these data and summarize your findings. (5 pts.)
3. Ranks of Police Officers in the NYPD and Gender
The table below shows the rank attained by male and female officers in the New York City Police Department. Do these data indicate that men and women are equitably represented at all levels of the department? Data File: NYPD Gender
GenderRank / Male / Female / Row Total
Officer / 21,900 / 4,281 / 26,181
Detective / 4,058 / 806 / 4864
Sergeant / 3,898 / 415 / 4313
Lieutenant / 1,333 / 89 / 1422
Captain / 359 / 12 / 371
Higher ranks / 218 / 10 / 228
Column Totals / 31,766 / 5,613 / 37,379
a) What’s the probability that a police officer selected at random from the NYPD is a female? (1 pt.)
b) What’s the probability that a police officer selected at random is a detective? (1 pt.)
c) Assuming no bias in promotions, how many female detectives would you expect
NYPD to have? (1 pt.)
d) Is this a test of independence or homogeneity? Explain. (2 pts.)
e) Perform the appropriate test and summarize your findings. (5 pts.)
f) Other factors do you think should be considered investigating potential gender discrimination when it comes to rank of officers in the NYPD? (2 pts.)
4. Lead Exposure Amongst Children in El Paso, TX and IQ Scores
The paper "Neuropsychological Dysfunction in Children with Chronic Low-Level Lead Absorption" published in Lancet, 1, pp. 708-715, March 1975 examined the effects of exposure to lead on the psychological and neurological well-being of children. In summary, a group of children who lived near a lead smelter in El Paso, Texas, were identified and their blood levels of lead were measured. An “High Lead” group of 46 children were identified who had blood-lead levels 40 micrograms/milliliter in 1972 (or in few cases 1973). A “Low Lead” group of 78 children was also identified with blood-lead levels < 40 micrograms/milliliter in both 1972 and 1973. All children in the study lived in close proximity to the lead smelter.
One of the questions of interest to the researchers was whether the children with high lead levels (“High Lead” group) had a lower mean performance IQ score than children with less elevated lead levels (“Low Lead” group). The data for examining this issue are contained in the file: Lead-IQ.JMP.
a) Would you be willing to assume that the variance in the IQ scores is same for both populations? Explain. (2 pts.)
b) Do the IQ scores for both groups of children appear to be normally distributed?(2 pts.)
c) Do these data provide evidence those with a lesser degree of lead exposure have higher mean IQ scores than those with higher lead levels? (5 pts.)
d) Report and interpret a 95% confidence interval for the difference in mean IQ scores for these two groups of children. (3 pts.)
Problem 5–Respiration Sinus Arrhythmia in Psychotic Children
Piggot et al. paired 10 psychotic and 10 normal children (controls) by matching them on both age and gender. They compared the subjects for differences in respiratory sinus arrhythmia under conditions of spontaneous and 5-, 10-, and 15-second interval breathing. They recorded the cardiac rate and respiratory changes simultaneously. The table below shows the differences in duration of the cardiac acceleratory phase following the beginning of inspiration (psychotics compared to the controls for the third respiration).
PAIR / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10Psychotic / 1.74 / 1.44 / 2.12 / 1.80 / 2.00 / 2.70 / 1.96 / 1.46 / 1.82 / 1.40
Control / 2.46 / 1.88 / 2.38 / 1.94 / 2.14 / 1.60 / 1.96 / 1.82 / 1.80 / 1.84
Do these data provide sufficient evidence to indicate a difference between the means for psychotic and normal children? Use the test you feel is most appropriate for answering this question and summarize your findings. (5 pts.)
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