Both before and after a recent earthquake, surveys were
conducted asking voters which of the three candidates they planned
on voting for in the upcoming city council election. Has here been
a change since the earthquake? You are conducting a Test of
Independence for the claim that there is an association
between the earthquake and the voter support at α=0.05α=0.05. The
following table summarize the result of the survey.
Perez | Chung | Stevens | |
---|---|---|---|
Before | 38 | 27 | 37 |
After | 22 | 17 | 27 |
Perez | Chung | Stevens | |
---|---|---|---|
Before | |||
After |
χ²-Test for independence
below is expected value table:
Expected | Ei=row total*column total/grand total | Perez | Chung | Stevens |
before | 36.4 | 26.7 | 38.9 | |
after | 23.6 | 17.3 | 25.1 |
Applying chi square test of independence: |
chi square χ2 | =(Oi-Ei)2/Ei | Perez | Chung | Stevens | Total |
before | 0.068 | 0.003 | 0.089 | 0.1596 | |
after | 0.105 | 0.0047 | 0.1372 | 0.2467 | |
total | 0.1725 | 0.0078 | 0.2259 | 0.406 | |
test statistic X2 = | 0.406 |
The p-value for this sample = 0.8162
The p-value is greater than alpha
fail to reject the null hypothesis
The sample data suggests there is not sufficient evidence to conclude the claim that there is an association between the earthquake and the voter support at α=0.05
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