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 95% 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.Take SampleNumber of patients Sample mean Sample standard deviationPopulation standard deviation1.68Enter 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 95% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".Confidence level Critical value99% =z0.0052.57695% =z0.0251.96090% =z0.0501.645Sample size:Point estimate:Population standard deviation:Critical value:ComputeStandard error:Margin of error:95% confidence interval:(b)Based on your sample, enter the lower and upper limits to graph the 95% confidence interval for the population mean of the surgery durations for all brain tumor patients.95% confidence interval:0.002.004.006.008.0010.00
Question
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 95% 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.Take SampleNumber of patients Sample mean Sample standard deviationPopulation standard deviation1.68Enter 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 95% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".Confidence level Critical value99% =z0.0052.57695% =z0.0251.96090% =z0.0501.645Sample size:Point estimate:Population standard deviation:Critical value:ComputeStandard error:Margin of error:95% confidence interval:(b)Based on your sample, enter the lower and upper limits to graph the 95% confidence interval for the population mean of the surgery durations for all brain tumor patients.95% confidence interval:0.002.004.006.008.0010.00
Solution
I'm sorry, but your question seems to be incomplete. You've provided a scenario and some instructions, but you haven't provided the sample mean or the sample size.
However, I can guide you on how to calculate the 95% confidence interval based on the information you've given.
Here are the steps:
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Identify a sample statistic. Since we are trying to estimate a population mean, we choose the sample mean (x̄) as the sample statistic. You need to provide this value.
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Select a confidence level. In this analysis, the confidence level is defined for us in the problem. We are working with a 95% confidence level.
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Find the standard deviation or standard error. Since we do not know the standard deviation of the population, we cannot compute the standard deviation of the sample mean. Instead, we compute the standard error (SE). SE = s/sqrt(n), where s is the standard deviation of the sample and n is the sample size. In this case, the standard deviation is given as 1.68 hours.
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Find the margin of error. Elsewhere on this site, we show how to compute the margin of error when the sampling distribution is approximately normal. The key steps are shown below:
- Find standard deviation or standard error.
- Find the sample size, n.
- Multiply the result by the appropriate z*-value for the confidence level desired. The z*-value is found using a Z-table. For a 95% confidence level, the z*-value is 1.96.
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Specify the confidence interval. The range of the confidence interval is defined by the sample statistic plus the margin of error. The uncertainty is denoted by the confidence level.
Please provide the missing values so I can help you calculate the confidence interval.
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