Assignment for Chi Square Tests
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Middle Tennessee State University *
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3020
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Industrial Engineering
Date
Dec 6, 2023
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docx
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3
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Assignment for Chi-Square Tests
Scenario 1. Health Status of Young Adults
A researcher wanted to determine whether the proportions of young adults in the health status categories (Poor,
Good, Excellent) are the same. Three hundred young adults were classified based on their current health status.
The frequencies are reported below. Use an alpha = .05 to test the null hypothesis
by hand
. Show your work.
Frequency Distribution for Health Status of Young Adults
Poor
Good
Excellent
Total
80
130
90
300
State the null and alternative hypotheses.
Set the Criteria for a Decision
Alpha Level =
Degrees of Freedom =
Chi-Square Critical Value =
Calculation Worksheet for Chi-Square Test
Group
Observed
N
Theoretical
Proportion
Expected
N
Observed
N
−
Expected
N
(
Observed
N
−
E xpected N
)
2
Expected
N
Poor
Good
Excellent
Interpretation
Scenario 2. Health Status and Age for Young Adults
A researcher wanted to determine whether health status (Poor, Good, Excellent) and age are related for young
adults. Three hundred young adults were classified based on their current health status and age group. The
frequencies are reported below. Use an alpha = .05 to test the null hypothesis
by hand
. Show your work.
Table 1
Frequency Distribution for Health Status and Age Group of Young Adults
Health Status
Poor
Good
Excellent
Tota
l
Twenties
25
65
75
165
Age
Group
Thirties
35
55
45
135
Total
60
120
120
300
State the null and alternative hypotheses.
Set the Criteria for a Decision
Alpha Level =
Degrees of Freedom =
Chi-Square Critical Value =
Calculation Worksheet for Chi-Square Test
Age
Health
Observe
d
N
Expected
N
Obs
N
−
Exp
N
(
Observed
N
−
E xpected N
)
2
Expected
N
Twenties
Poor
Twenties
Good
Twenties
Excellen
t
Thirties
Poor
Thirties
Good
Thirties
Excellen
t
Interpretation
Background Information for Scenarios 3 and 4
The assignments used in the class are based on a
subset of data
from the Survey of Texas Adults, 2004
(ICPSR4297). Large-scale data sets often use a weighted sampling technique to obtain a representative sample
of the population while oversampling subgroups to ensure all subgroups have sufficient sample size. The
examples used in class do not take into account the weighted sampling methodology. I also used a stratified
sampling technique to ensure there were equal sample sizes based on A001 (Vote) and A020 (Political
Affiliation).
Musick, Marc A. Survey of Texas Adults, 2004. Inter-university Consortium for Political and Social Research
[distributor], 2005-09-22.
https://doi.org/10.3886/ICPSR04297.v1
Scenario 3 – Highest Degree Earned
A researcher wanted to determine whether the proportions of Texans in the highest degree earned categories
(H006: HS Degree, Associate, Bachelor) are the same in the Survey of Texas Adults, 2004 (ICPSR4297) data
set. Use an alpha of .05 to test the null hypothesis.
Use jamovi to conduct the analysis.
Select
Analyses → Frequencies →
N
Outcomes (Chi-Square Goodness of Fit)
Paste the proportions table produced by jamovi below.
Interpret the results using the format we practiced in class.
State the null and alternative hypotheses.
Jamovi table
Interpretation
Scenario 4 – Spanish/Hispanic Descent and Voting Status
A researcher wanted to determine whether Spanish/Hispanic Descent (H002: No, Yes) and vote status (A001:
No, Yes) for the past election are related in the Survey of Texas Adults, 2004 (ICPSR4297) data set. Use an
alpha of .05 to test the null hypothesis.
Use jamovi to conduct the analysis.
Select
Analyses → Frequencies → Independent Samples (χ
2
test of association)
Paste the contingency table produced by jamovi below. The contingency table should include counts and
row percentages.
Interpret the results using the format we practiced in class.
State the null and alternative hypotheses.
Jamovi table
Interpretation
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