Question 2: Now consider the relationship between the categorical variables GPA, Gender and Length of Time in School District separately of Candidate Preference. a) If GPA is statistically independent of the length of time living in the school district, fill in the expected cross-tabulation data table below. GPA 3.5 GPA 3.5 Live in School District > 5 years Live in School District < 5 years Total Consider the observed cross-tabulation data table below. Live in School District 5 years Live in School District < 5 years Total = Male Female Total 148 Male Female Total 148 GPA 3.5 GPA 3.5 123 25 148 Compute the statistic T (Observed-Expected;)2 Expected; for the cross-tabulated data above. Does the data indicate that GPA is statistically independent of the length of time living in the school district? b) If gender is statistically independent of GPA, fill in the expected cross-tabulation data table below. 67 81 148 252 GPA 3.5 GPA 3.5 Total 183 217 400 Consider the observed cross-tabulation data table below. 252 152 100 252 GPA 3.5 GPA 3.5 Total 183 217 400 116 136 252 Total 275 125 400 Total 275 125 400 Compute the statistic T = Σ (Observed-Expected;)² Expected; Does the data indicate that GPA is statistically independent of gender? for the cross-tabulated data above.
Question 2: Now consider the relationship between the categorical variables GPA, Gender and Length of Time in School District separately of Candidate Preference. a) If GPA is statistically independent of the length of time living in the school district, fill in the expected cross-tabulation data table below. GPA 3.5 GPA 3.5 Live in School District > 5 years Live in School District < 5 years Total Consider the observed cross-tabulation data table below. Live in School District 5 years Live in School District < 5 years Total = Male Female Total 148 Male Female Total 148 GPA 3.5 GPA 3.5 123 25 148 Compute the statistic T (Observed-Expected;)2 Expected; for the cross-tabulated data above. Does the data indicate that GPA is statistically independent of the length of time living in the school district? b) If gender is statistically independent of GPA, fill in the expected cross-tabulation data table below. 67 81 148 252 GPA 3.5 GPA 3.5 Total 183 217 400 Consider the observed cross-tabulation data table below. 252 152 100 252 GPA 3.5 GPA 3.5 Total 183 217 400 116 136 252 Total 275 125 400 Total 275 125 400 Compute the statistic T = Σ (Observed-Expected;)² Expected; Does the data indicate that GPA is statistically independent of gender? for the cross-tabulated data above.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Assessing Statistical Independence in a Categorical Data Set
Answer A & B
Transcribed Image Text:Question 2: Now consider the relationship between the categorical variables GPA,
Gender and Length of Time in School District separately of Candidate Preference.
a) If GPA is statistically independent of the length of time living in the school district,
fill in the expected cross-tabulation data table below.
Live in School District > 5 years
Live in School District < 5 years
Total
148
Consider the observed cross-tabulation data table below.
Live in School District > 5 years
Live in School District < 5 years
Total
Male
Female
Total
GPA 3.5 GPA 3.5 Total
275
125
400
Male
Female
Total
148
GPA 3.5 GPA 3.5
123
25
148
Compute the statistic T =
(Observed-Expected;)2
Expected,
for the cross-tabulated data above.
Does the data indicate that GPA is statistically independent of the length of time living
in the school district?
b) If gender is statistically independent of GPA, fill in the expected cross-tabulation
data table below.
67
81
148
252
GPA 3.5 GPA 3.5 Total
183
217
400
Consider the observed cross-tabulation data table below.
GPA 3.5 GPA 3.5
252
152
100
252
116
136
252
Total
275
125
400
Total
183
217
400
Compute the statistic T =
(Observed,-Expected) for the cross-tabulated data above.
Expected
Does the data indicate that GPA is statistically independent of gender?
Expert Solution
Step 1
A chi-square (Χ2) test of independence is a type of Pearson’s chi-square test. The Pearson's chi-square tests is a nonparametric tests used for categorical variables. We use a chi-square test of independence, to determine whether two categorical variables are related or not. This test compares the observed frequencies to the expected frequencies if the two variables are not related. When the variables are not related, the observed and expected frequencies will be homogeneous.
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