Comparative Analysis for Two and Several Populations (38 ...



Comparative Analysis for Two Populations (48 points)

1 - Risk Factors for Having a Child with Low Birth Weight

Data File:  Lowbirth.JMP in the Anova/t-test JMP folder

The purpose of this study was to identify potential risk factors for low birth weight.   A random sample of new mothers was taken and the birth weight was recorded.  Also the following categorical variables were measured: previous history of premature labor (Prev?), hypertensive during pregnancy (Hyper?), smoking status during pregnancy (Smoke?), uterine irritability during pregnancy (Uterine), and minority status (Minority).   Use comparative methods to compare the mean birth weights across the levels of these five factors.  Which factors have the largest birth weight differences? Use both hypothesis tests and confidence intervals to justify your conclusions.  Summarize your findings in a clearly written paragraph. (20 pts.)

(NOTE: 1 lb. = 454 grams, so if you divide the birth weight column by 454 you will have birth weight in pounds.)

2 - National Inmate Survey

These data come from a survey of inmates held in U.S. Prisons in 1997. In the survey inmates were asked a large number of questions pertaining to their arrest record, previous offenses, parole history, etc. The variables here represent a small subset of the information recorded.

The variables in this data file Inmate Survey.JMP are:

ID - identification number

Gender – Men or Women

Age - age of inmate

Race - 1 = white, 2 = black, 3 = asian, 4 = hispanic, 5 = native american

Minority – Minority or Non-Minority

Armed Forces – AF or No AF

Hired Own Lawyer – Hired Lawyer or No

Found Guilty – Found Guilty or No

Sentence Length - length of sentence (yrs.)

log(Length) - log base 10 of the sentence

Notes on Log Transformations in Comparative Analyses:

a) Construct a confidence interval for the mean sentence length of all inmates surveyed. Give the correct interpretation of this interval. Also perform a hypothesis test to determine if the mean sentence length of inmates in U.S. prisons exceeds 10 years. (4 pts.)

b) Find a 95% confidence interval for the median sentence length of prisoners in the U.S. Interpret this interval. Which interval, this one or the interval from part (a), gives a better representation of the typical length of sentence for U.S. inmates? Explain. (4 pts.)

c) Use the comparative procedures to determine if the length of sentence differs between men and women inmates. If a difference exists describe the nature of the difference. Give a 95% confidence interval for the difference in the typical length of sentence between men and women inmates. Does this survey suggest that women receive more lenient sentencing than men? Explain. (4 pts.)

d) Is there a significant difference in the typical sentence length between minorities and non-minorities? Use comparative methods to answer this question. (4 pts.)

e) Is there a significant difference in the typical length of sentence between inmates who served in the armed forces and those who did not? If there is a difference, conjecture why this may be the case. (4 pts.)

f) Use comparative methods to determine if there are differences in the typical length of sentence between those that were found guilty in a trial and those that plead guilty or non-contest. (4 pts.)

g) To examine determine if the typical length of sentence depends on the whether the inmate was assigned or hired their own lawyer. Discuss your findings. (4 pts.)

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