Question: Last year the city of Bellingham in Selina County, Georgia, undertook a campaign to consolidate the city and county governments. The premise was that proportionately more people in the city would favor the concept than in outlying county area; this was because the county people might expect a tax increase from the consolidation even though the proponents of the plan promised a tax reduction in the long run. A polling agency was hired to conduct a study of this issue. It randomly selected 100 people in the city and 75 people in the county. It found 62 city dwellers and 36 county dwellers favoring the plan. Develop and interpret a \(98 \%\) confidence interval for difference of population proportions that favor consolidating the city and county governments.

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