Homework SourseA survey of voter sentiment was conducted in four midcity po
A survey of voter sentiment was conducted in four midcity political wards to compare the fraction of voters favoring candidate A. random samples of 200 voters were polled in each of the four wards with results as shown.
Ward 1
Ward 2
Ward 3
Ward 4
Totals
Favor A
76
53
59
48
236
Not Favoring A
124
147
141
152
564
Totals
200
200
200
200
800
Do the data present sufficient evidence to indicate that the fractions of voters favoring candidate A differ in the four wards? (Test the Hypothesis of independence of the two classifications using alpha = 0.05).
| Ward 1 | Ward 2 | Ward 3 | Ward 4 | Totals | |
| Favor A | 76 | 53 | 59 | 48 | 236 |
| Not Favoring A | 124 | 147 | 141 | 152 | 564 |
| Totals | 200 | 200 | 200 | 200 | 800 |
Solution
We will use Chi Square test of independence...
10.72
Chi-square value=10.72
Critical region = 7.82
Since the calculated value 10.72 is greater than tabulated value of 7.82 with 3 degrees of freedom, we can conclude that the fractions of voters favoring candidate A differ in the four wards.
| Observed(O) | Expected E | (O-E) | (O-E)2 /E |
| 76 | 59 | 17 | 4.90 |
| 53 | 59 | -6 | 0.61 |
| 59 | 59 | 0 | 0.00 |
| 48 | 59 | -11 | 2.05 |
| 124 | 141 | -17 | 2.05 |
| 147 | 141 | 6 | 0.26 |
| 141 | 141 | 0 | 0.00 |
| 152 | 141 | 11 | 0.86 |
| 10.72 |
