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Comparing Two Categorical Variables
Data Sets Needed: Class Survey and HSB data sets
1: Sleep apnea is a pattern of irregular breathing during sleep, with longer than normal breath-holding
intervals. The following two-way table shows counts of men and women with sleep apnea or not, from a
sleep study with 400 men and 300 women.
Sleep Apnea?
Gender
Men
Women
Yes
40
12
No
360
288
a. Calculate the risk of sleep apnea for men in this study.
b. Calculate the risk of sleep apnea for women in this study.
c. Find the value that completes this sentence: The risk of sleep apnea for men is ___ times the risk for
women. In other words, determine the relative risk.
d. Find the value that completes this sentence: The odds of sleep apnea for men are __ times the odds for
women. In other words, find the odds ratio.
2: Use Class Survey data set and Stat>Tables>CrossTabulation and Chi-Square to answer the
following questions. Put Gender (C2) in the row and the variable Ever Cheat (C14) in the column and be
sure the check box for COUNTS and ROW PERCENTS are selected. [The variable Ever Cheat is student
responses to whether they ever cheated on a significant other]
a. Fill in this table with row percents.
Ever Cheat
Gender
No
Yes
Female
Male
b. Explain why the table of row percents indicates that there is a weak or no relationship between gender
and whether students cheated on a significant other.
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c. Do a chi-square test for statistical significance of independence of the observed relationship. Return to
Stat>Tables>CrossTabulation and Chi-Square and now select the tab Chi-Square and select the box
for Chi-Square Analysis.
(i) Give p-value for the test,
(ii) explain whether the observed relationship is statistically significant and why
(iii) state a general conclusion.
3 Using the HSB data: The High School and Beyond data is from a large-scale longitudinal
study conducted by the National Opinion Research Center (1980) under contract with the
National Center for Education Statistics. Below is a table (note: this is called summarized
data!) representing a sample of 100 students from this data that includes the student’s gender
and whether the high school they attended was public or private. Note: if you did the activity for
the probability lesson this would be a test of independence: that is, can we say that the probability of
being Female is independent of the probability that school type is public? [Go back to part 2 for Minitab
steps.]
Female
Male
Total
(i)
Public
38
46
84
Private
7
9
16
Total
45
55
100
include a relevant table of conditional percents (complete following table using percents
where conditional percents are row percents),
Public
Private
Total
Female
Male
Total
(ii)
based on the percents, discuss the nature of any relationship, and
(iii)
do a chi-square test of statistical significance. State a clear conclusion for the test of
significance.
4: Suppose a newspaper article states that drinking three or more cups of coffee doubles the risk
of gall bladder cancer. Before giving up coffee, what question(s) should be asked by a person
who drinks this much coffee? (There is more than one possible answer.)
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