Question

Out of 200 people sampled, 182 preferred Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A. Use a 99% confidence level, and give your answers as decimals, to three places.

Answer 1

At a 99% confidence level, the estimated proportion (p) of the voting population that prefers Candidate A is approximately 0.910.

Step-by-step explanation:

Given a sample of 200 people where 182 preferred Candidate A, the sample proportion (p) is calculated as 182/200 = 0.910.

Determine the standard error (SE) using the formula SE = sqrt[(p(1-p))/n], where n is the sample size.

Given a 99% confidence level, the critical z-value is approximately 2.576.

Calculate the margin of error (ME): ME = 2.576 * SE.

Calculate the confidence interval: p ± ME.

Express the result in decimal form: 0.910 ± 0.045.

Therefore, the estimated proportion (p) of the voting population that prefers Candidate A is approximately 0.910.