PROBLEM 15

LIKLIHOOD RATIO TESTS

On page 485, Mendenhall, Scheaffer, and Wackerly present the following problem (10.75):

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 significance level.

WARD FAVOR DO NOT FAVOR

1 76 124

2 53 147

3 59 141

4 48 152

To fulfill the requirements of this problem, solve Mendenhall, et al's problem on the computer using SAS. Using PROC FREQ with the CHISQ option, this will be a chi-square test with m-1 degrees of freedom where m is the number of groups (m=4 in this case, so df=3). Create a new dataset called TEST.CNTL and input the following JCL, SAS commands, and data:

//GABCDE1 JOB (AF,A591),yourname,REGION=1024K

/*OPENBIN

//S1 EXEC SAS

//SYSIN DD *

DATA PROB15;

INPUT WARD$ OPINION$ COUNT @@;

CARDS;

WARD1 FAVOR 76 WARD1 DISFAVOR 124

WARD2 FAVOR 53 WARD2 DISFAVOR 147

WARD3 FAVOR 59 WARD3 DISFAVOR 141

WARD4 FAVOR 48 WARD4 DISFAVOR 152

PROC FREQ;

WEIGHT COUNT;

TABLES WARD*OPINION/CHISQ;

//

WRITING UP YOUR PROGRAM

Write up your explanation of the statistical results on your computer output before turning it in.

- Symbolically, what are the null and alternative hypotheses?

- What is the formula for obtain the chi-square test statistic ?

- Draw a graph of the chi-square and indicate the critical value, the test

statistic and the prob value (by shading and indicating the amount of the shaded area).

- Do you reject the null hypothesis?

- What do you conclude?

- What other tests could you have performed on these data?

- Could you use a paired t-test to answer a different question?

- What would that question be?

- Explain the difference.