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E Confidence Intervals and Hypothesis Testing Introduction to constructing a confidence interval for a population mean.. 13 Kersten V V Espanol You are a data analyst for a health insurance company and want to estimate the population mean of the surgery durations for all brain tumor patients. To do so you select a random sample of 32 brain tumor surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all brain tumor surgeries is 1.68 hours Based on your sample, follow the steps below to construct a 90% confidence interval for the population mean of the surgery durations for all brain tumor patients. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 32 brain tumor patients. Number of patients Sample mean Sample standard Population standard deviation deviation Take Sample 32 3.18 1.53 1.68 Enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 90% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". Sample size: X Standard error: Point estimate: Population standard deviation: Margin of error: Confidence level Critical value Explanation Check @ 2025 McGraw Hill. Terms of Use | Privacy Center | Accessibility 90% confidence interval: 95% 20.025 = 1.960 Compute 90% Z0.050 = 1.645 (b) Based on your sample, enter the lower and upper limits to graph the 90% confidence interval for the population mean of the surgery durations for all brain tumor patients. 0.00 10.00 0.00 2.00 4.00 6.00 8.00 10.00 X