Based on the calculations, the 95% confidence interval of E(Y) is equal to 52.3% ± 3.26%.
Mathematically, a confidence interval of 95% is given by;
α = 1 - 0.95
α = 0.05.
α/2 = 0.05/2 = 0.025.
Next, we would determine the standard deviation of the mean:
Standard deviation of mean = 50/√800
Standard deviation of mean = 1.77.
From the z-table, the z-score of a 95% confidence interval is equal to 1.96.
Confidence interval (0.05, 50, 800) = 1.77 × 1.96
Confidence interval (0.05, 50, 800) = 3.46.
Mathematically, the confidence interval for a mean is given by:
Mean ± (t-critical × (standard deviation/√(sample size)))
Confidence interval = 52.3% ± 3.26%.
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Complete Question:
A research team studied Y, the percentage of voters in favor of a candidate. The random variable Y had standard deviation o = 50%. A random sample of 800 voters was selected, and their average was y-bar(800) = 52.3%. What is the 95% confidence interval for E(Y)?
