If a sample with a standard deviation of 20 has a confidence interval of approximately 11.14

Question

If a sample with a standard deviation of 20 has a confidence interval of approximately 11.14 < μ < 24.86, what would the most likely sample size be?

Quizplus · Accepted Answer

The confidence interval is given by:μ ± z * (σ / √n)where:μ is the population meanσ is the population standard deviationn is the sample sizez is the z-score corresponding to the desired confidence levelIn this case, we have:11.14 < μ < 24.86σ = 20z = 1.96 (for a 95% confidence level)Solving for n, we get:n = (z * σ / (μ - μ))^2= (1.96 * 20 / (24.86 - 11.14))^2= 36Therefore, the most likely sample size is 36.

If a Sample with a Standard Deviation of 20 Has