A prominent medical group claims that the population mean of the surgery durations for all brain tumor patients is 3.69 hours. You are a data analyst for a health insurance company and want to test that claim. 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 99% confidence interval for the population mean of the surgery durations for all brain tumor patients. Then state whether the confidence interval you construct contradicts the medical group’s claim. (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.Table:- Number of patients: 32- Sample mean: 3.29- Sample standard deviation: 1.24- Population standard deviation: 1.68Instructions: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 99% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".- Sample size:- Point estimate:- Population standard deviation:- Critical value:Output:- Standard error:- Margin of error:- 99% confidence interval:Critical values:- \( z_{0.005} = 2.576 \)- \( z_{0.010} = 2.326 \)- \( z_{0.025} = 1.960 \)- \( z_{0.050} = 1.645 \)- \( z_{0.100} = 1.282 \)(b) Based on your sample, graph the 99% confidence interval for the population mean of the surgery durations for all brain tumor patients.- Enter the lower and upper limits on the graph to show your confidence interval.- For the point (\(\star\)), enter the medical group’s claim of 3.69 hours.Graph:- 99% confidence interval: \( 0.00 \) to \( 10.00 \)(c) Does the 99% confidence interval you constructed contradict the medical group’s claim? Choose the best answer from the choices below

The objective is to obtain the confidence interval for the "true average surgery duration of brain…

A prominent medical group claims that the population mean of the surgery durations for all brain tumor patients is 3.69 hours. You are a data analyst for a health insurance company and want to test that claim. 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 99% confidence interval for the population mean of the surgery durations for all brain tumor patients. Then state whether the confidence interval you construct contradicts the medical group's claim. (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. (c) Take Sample Sample size: 0 Point estimate: 0 Population standard deviation: 0 Critical value: 0 Compute 0.00 0.00 Number of patients 32 2.00 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 99% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". Sample mean 4.00 Standard error: 3.29 Margin of error: 99% confidence interval: 99% confidence interval: 5.00 6.00 Sample standard (b) Based on your sample, graph the 99% confidence interval for the population mean of the surgery durations for all brain tumor patients. • Enter the lower and upper limits on the graph to show your confidence interval. . For the point (◆), enter the medical group's claim of 3.69 hours. 8.00 deviation 1.24 X Ś Critical values 20.005 = 2.576 20.010 =2.326 20.025 = 1.960 20.050 = 1.645 20.100 = 1.282 10.00 10.00 Population standard O No, the confidence interval does not contradict the claim. The medical group's claim of 3.69 hours is outside the 99% confidence interval. deviation O Yes, the confidence interval contradicts the claim. The medical group's claim of 3.69 hours is inside the 99% terval. con 1.68 Does the 99% confidence interval you constructed contradict the medical group's claim? Choose the best answer from the choices below. O No, the confidence interval does not contradict the claim. The medical group's claim of 3.69 hours is inside the 99% confidence interval. O Yes, the confidence interval contradicts the claim. The medical group's claim of 3.69 hours is outside the 99% confidence interval.