A few weeks before the senatorial election between incumbent

A few weeks before the senatorial election between incumbent Senator Smirk and his challenger, former Governor Graft, the senator?s polling organization wants to know where he should concentrate his campaigning. They take simple random samples of potential voters in the southern and northern portions of the state, and ask them if they have decided who to vote for or are still undecided. Here are the results: (a) Do these data provide convincing evidence that there is a difference the distribution of voters who have decided or are still undecided in the two regions? Use a chi-square test to support your conclusion.

Solution

Set up null and alternate as follows:

H0: The choice is independent of the region.

Ha: There is association between region and preferences.

Chi square statistic = 2.9302

p value = 0.0869

p value >0.05

The result is not significant at 0.05

Accept null hypothesis.

Results
	Category 1	Category 2				Row Totals
Group 1	116  (123.57)  [0.46]	60  (52.43)  [1.09]				176
Group 2	148  (140.43)  [0.41]	52  (59.57)  [0.96]				200
Column Totals	264	112				376  (Grand Total)