A Gallup poll conducted on September 3-5, 2012, surveyed 755 likely voters; 405

Question

A Gallup poll conducted on September 3-5, 2012, surveyed 755 likely voters; 405 reported a preference for President Barak Obama, and 350 reported a preference for Mitt Romney. A Gallup poll conducted on October 1-3, 2012, surveyed 756 likely voters; 378 reported a preference for Obama, and 378 reported a preference for Romney.

a. Construct a 95% confidence interval for the fraction of likely voters in the population who favored Obama in early September 2012.

b. Construct a 95% confidence interval for the fraction of likely voters in the population who favored Obama in early October 2012.

c. Was there a statistically significant change in voters’ opinions across the two dates?

Explanation / Answer

(a) For 95% CI, z = 1.65

Margin of Error, ME = z*sqrt(p*(1-p)/n) = 1.65 * sqrt(0.536 * ( 1 - 0.536)/755) = 0.0299

Confidence Interval = (p-ME, p+ME) = (0.506, 0.566)

(b)

Margin of Error, ME = z*sqrt(p*(1-p)/n) = 1.65 * sqrt(0.5 * ( 1 - 0.5)/756) = 0.03

Confidence Interval = (p-ME, p+ME) = (0.470, 0.530)

(c)

yes the change is significant, becasue in septmber from the confidence interval we can reject the claim that Barak Obama has less than 50% of majority but in case of October survey we can not reject the same claim.

September 3-5, 2012 October 1-3, 2012 Total 755 756 Obama 405 378 Romney 350 378 p 0.536 0.5

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