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A survey of voter sentiment was conducted in four midcity
Chapter 10, Problem 106E(choose chapter or problem)
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 the results as shown in the accompanying table. The numbers of voters favoring A in the four samples can be regarded as four independent binomial random variables.
Construct a likelihood ratio test of the hypothesis that the fractions of voters favoring candidate A are the same in all four wards. Use \(\alpha=.05\).
Ward |
|||||
Opinion |
1 |
2 |
3 |
4 |
Total |
Favor A |
76 |
53 |
59 |
48 |
236 |
Do not favor A |
124 |
147 |
141 |
152 |
564 |
Total |
200 |
200 |
200 |
200 |
800 |
Equation transcription:
Text transcription:
\alpha=.05
Questions & Answers
QUESTION:
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 the results as shown in the accompanying table. The numbers of voters favoring A in the four samples can be regarded as four independent binomial random variables.
Construct a likelihood ratio test of the hypothesis that the fractions of voters favoring candidate A are the same in all four wards. Use \(\alpha=.05\).
Ward |
|||||
Opinion |
1 |
2 |
3 |
4 |
Total |
Favor A |
76 |
53 |
59 |
48 |
236 |
Do not favor A |
124 |
147 |
141 |
152 |
564 |
Total |
200 |
200 |
200 |
200 |
800 |
Equation transcription:
Text transcription:
\alpha=.05
ANSWER:
Step 1 of 6
Let us denote as the number of people in the sample of 200 who are in favor of A.
We have
following Binomial distribution with and unknown.