STAT 477/577 - Homework Assignment 5

STAT 477/577 - Homework Assignment 5

General homework guidelines: All homework assignments should be submitted using Canvas.
Please submit your answers separately, for each of the problems, as set-up in the Canvas submission portal.
You are allowed to either type in your answers, as well as submit graphs directly, within each submission
item. You are also allowed to submit a scanned copy of your answer, as long as the answers are submitted
separately for each question, as instructed. You can either scan your answers (ask if you don’t have access to
a scanner or do not know how to use your phone to do so), or just submit a picture of your answer. Please
note that if we can’t read your answer, we won’t be able to award any (partial) credit.
You have one attempt to submit your answers. If technical issues appear and your submission portal
has closed for some reason, please email Prof. Caragea explaining the situation and requesting permission
to resubmit. Please note that such requests must be made before the deadline.
Please note that for this homework only I have changed the due date from Tuesday to Thursday, and
there is no grace period for late submissions with penalty. The due date of Thursday, March 24 is firm and
final. No submissions will be accepted past this date.
Homework problems.
1. [6 pts.] The following table of counts was obtained from a random sample of 1397 respondents from
the population of adults (more than 18 years old) in the United States in 1982. Each respondent
was cross-classified with respect to opinions regarding gun registration as a part of comprehensive gun
control legislation and imposing the death penalty on adults convicted of certain violent acts.
Death Penalty
Gun Registration Favor Oppose Total
Favor 784 236 1020
Oppose 311 66 377
Total 1095 302 1397
(a) Conduct a test of independence for the two variables. You may use R to answer this question, as
long as you clearly explain/show how you obtained your results.
(b) Calculate the correlation (φ) coefficient for the two variables.
2. [9 pts.] The operations manager of a company that manufactures tires wants to determine whether
there are any differences in the quality of workmanship among the three daily shifts. She randomly
selects 496 tires and carefully inspects them. Each tire is either classified as perfect or non-perfect,
and the shift that produced it is also recorded. The two categorical variables of interest are: shift and
condition of the tire produced. The data can be found in the file tires.csv.
(a) Explain why it is reasonable to conduct a test of independence for these two variables even though
the shift variable is a grouping variable.
(b) Describe a different data collection that would have required the use of a test for the equality of
proportions.
(c) Use R to create a contingency table and mosaic plot for the two variables and write a description
of their relationship.
(d) Conduct a test of independence for the two variables. Clearly write the hypotheses, the value of
the test statistics and the p-value, along with your conclusions.
(e) Calculate the φ coefficient and Cramer’s V for this contingency table. You may do this by hand
or using R.
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3. [10 pts.] In the 2002 General Social Survey of adults in the United States conducted by the National
Opinion Research Center, respondents were asked about their perceived happiness (Not Too Happy,
Pretty Happy, Very Happy) and their family income level (Below Average, Average, Above Average).
The data can be found in the file norc.csv.
(a) Use R to calculate a contingency table for the two variables.
(b) Calculate a test of independence for the two variables.
(c) Which two cells are concordant cells with the cell Very Happy - Average Income?
(d) Which two cells are discordant cells with the cell Pretty Happy - Below Average Income?
(e) Calculate the Goodman-Kruskal Gamma statistic for these data to determine the strength of the
directional relationship between the two variables and report its confidence interval. What does
this tell you about the directional relationship between perceived happiness and income of adults
in the United States?
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