A simple random sample of 80 items resulted in a sample mean of 70. The population standard deviation is σ = 5. (a) Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.) to (b) Assume that the same sample mean was obtained from a sample of 160 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.) to (c) What is the effect of a larger sample size on the interval estimate? A larger sample size provides a smaller margin of error. A larger sample size does not change the margin of error. A larger sample size provides a larger margin of error.
Added by Richard O.
Step 1
Given: Sample mean (x̄) = 70 Population standard deviation (σ) = 5 Sample size (n) = 80 Critical value (z) for 95% confidence level = 1.96 Margin of error (E) = z * (σ / √n) E = 1.96 * (5 / √80) E = 1.96 * (5 / 8.94) E = 1.096 Confidence interval = (x̄ - E, x̄ + Show more…
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