For a certain ballot issue, many county voters feel that theproposal will pass b

Question

For a certain ballot issue, many county voters feel that theproposal will pass because of the
large proportion of the city voters who favor the issue.

a) If 120 of 200 town voters favor the issue and 240 of 500 countyvoters favor the issue,
would you agree that the proportion of town voters favoring theissue is higher than the
proportion of county voters favoring the issue? Use a 0.025 levelof significance.

b) Establish a 99% Confidence interval about the difference in theproportion of the town
voters and county voters who favor the proposal
Hint: Assume p1= the true proportion of town voters who favor theissue and p2 = the true
proportion of county voters who favor the issue

Explanation / Answer

(a) Given p1=120/200=0.6 (town), n1=200                p2=240/500=0.48 (country), n2=500 The test hypothesis is Ho:p1p2 The test statistic is Z=(p1-p2)/([p1*(1-p1)/n1] + [p2*(1-p2)/n2]) = (0.6-0.48)/sqrt((0.6*(1-0.6)/200) + (0.48*(1-0.48)/500)) = 2.91 Given =0.025, Z(0.025)=1.96 (check normal table) Since Z=2.91>1.96, we reject Ho. So, I would agree that theproportion of town voters favoring the issue is higher than theproportion of county voters favoring the issue. ----------------------------------------------------------------------------------------------------------------------- (b) Given =0.01, Z(0.005)=2.58 (check normal table) The 99% CI is (p1-p2)±Z*([p1*(1-p1)/n1] + [p2*(1-p2)/n2]) -->(0.6-0.48)±2.58*sqrt((0.6*(1-0.6)/200) +(0.48*(1-0.48)/500)) --> ( 0.0136, 0.2264)

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