Out of 400 people sampled, 344 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.

Question

Out of 400 people sampled, 344 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.

Use a 95% confidence level, and give your answers as decimals, to three places.

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Answer 1

CI = sample proportion +/- z-critical value * standard error

sample proportion (phat) = 344/400 = 0.86

standard error = sqrt(phat*(1-phat)/sample size) = sqrt(0.86*0.14/400) = 0.01735

z-critical value (alpha/2 = 0.025, find z score for 0.975 probability) = 1.96

CI = 0.86 +/- 1.96* 0.01735

0.86+/-0.034 = 0.826, 0.894