For a 95% confidence interval of the mean with known sigma, observed x̄ = 52, sigma = 6, n = 64. What is the margin of error?

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Multiple Choice

For a 95% confidence interval of the mean with known sigma, observed x̄ = 52, sigma = 6, n = 64. What is the margin of error?

Explanation:
For a mean with known sigma, the margin of error is the z-score for the desired confidence level times the standard error. For 95% confidence, use the z value of 1.96. The standard error is sigma divided by the square root of n: 6 / sqrt(64) = 6 / 8 = 0.75. Multiply: 1.96 × 0.75 = 1.47. So the margin of error is 1.47. The observed x̄ = 52 centers the interval, which would be 52 ± 1.47 (i.e., (50.53, 53.47)).

For a mean with known sigma, the margin of error is the z-score for the desired confidence level times the standard error. For 95% confidence, use the z value of 1.96. The standard error is sigma divided by the square root of n: 6 / sqrt(64) = 6 / 8 = 0.75. Multiply: 1.96 × 0.75 = 1.47. So the margin of error is 1.47. The observed x̄ = 52 centers the interval, which would be 52 ± 1.47 (i.e., (50.53, 53.47)).

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