A random sample of 48 days taken at a large hospital shows that an average of 38 patients were treated in the emergency room (ER) per day. The standard deviation of the population is 4. a. Find the 95% confidence interval of the mean number of ER patients treated each day in the hospital b. Find the 95% confidence interval of the mean number of ER patients treated each day in the hospital if the standard deviation is 8 instead of 4.
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Step 1
Given: - Sample mean (X bar) = 38 - Population standard deviation (sigma) = 4 - Sample size (n) = 48 - Confidence level = 95% - Z-score for 95% confidence level = 1.96 Margin of error (E) = Z * (sigma / sqrt(n)) E = 1.96 * (4 / sqrt(48)) E = 1.96 * (4 / 6.928) E Show more…
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