4. Find the minimum sample size needed to estimate the percentage of Republicans

Question

4. Find the minimum sample size needed to estimate the percentage of Republicans among registered voters in California. Use a 0.03 margin of error, a confidence level of 95%, and assume that p and q are unknown. (4 pts) 5. In a survey of 1002 people, 70% said that they voted in a recent presidential election. Voting records show that 61% of eligible voters actually did vote. a) Find a 90% confidence interval estimate of the proportion of people who say that they voted. (4 pts) (2 pts) b) Are the survey results consistent with the actual voter turnout of 61%? Why or why not?

Explanation / Answer

4 Solution:- Given that 95% confidence interval Z0.005=1.96 , E=0.03

n = (Z/E)^2*p*q (p,q are unknown)

   n = (1.96/0.03)^2*0.5*0.5 = 1067.11

n = 1067

5 solution:-

a) p = 0.70, q = 0.30

E = z*sqrt[(p)(q)/n]
= 1.645*sqrt[(0.7)(0.3)/1002]
= 0.0238

90 % Confidence interval : (0.70 - 0.0238 , 0.70 + 0.0238)
= (0.6762 , 0.7238)

b) No, because 61% does not fall in the confidence interval range of values for p.

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