Assume a Gallup Poll is doing a randomizd political survey to estimate the true

Question

Assume a Gallup Poll is doing a randomizd political survey to estimate the true percentage of Americans who would give the U.S. president a favorable rating in job performance. Knowing that the sample size is 966 participants and that 53% of those surveyed gave the president a favorable rating, calculate a 95% confidence interval for the true percentage of all Americans who would give a favorable rating for the president (46.37%, 59.63%) 0 (48.67%, 57.33%) O (52.9%, 53.10%) 47.07%, 58.93%) 0 (49.77%, 56.23%)

Explanation / Answer

Sol:

z crit for 95%=1.96

p^=53%=0.53

n=966

95% confidenc einterval for population proportion=

p^-zsqrt(p^(1-p^)/n,p^+zsqrt(p^(1-p^)/n

0.53-1.96sqrt(0.53*(1-0.53)/966),0.53+1.96*sqrt(0.53(1-0.53)/966)

0.4985,0.5615

49.85%,56.15%

OPTION E

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