\"Gallup conducted a survey in April 1 to 25, 2010, to determine the congression

Question

"Gallup conducted a survey in April 1 to 25, 2010, to determine the congressional vote preference of the American voters. They found that 51% of the male voters preferred a Republican candidate to a Democratic candidate in a sample of 5,490 registered voters. Gallup asks you, their statistical consultant, to tell them whether you could declare the Republican candidate as the likely winner of the votes coming from men if there was an election today. What is your advice? Why? Need to answer this question in terms of using confidence intervals.

Explanation / Answer

p = 0.51

standard error, s = sqrt(p(1-p)/N) = sqrt(0.51*0.49/5490) = 0.006746786

Zcrit = +/-1.96 for 95% Confidence interval

95% CI = 0.51 +/- 1.96*0.006746786 = (0.4968, 0.5232))

Since 0.5 is there in the confidence interval, we cannot conclude the republican cadidate is the likely winner.

Should increase the campaign effort to get a bigger vote base.

Since the p-value is greater than 0.5, we cannot reject the null hypothesis and there is not enough evidence to suggest declaring the republican candidte as the likely winner

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