A survey of voter sentiment was conducted in four midcity

Chapter 10, Problem 106E

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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

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.

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