If Xbar=81​,S=20​,and n=36​,and assuming that the population is normally​ distributed, construct a 90% confidence interval estimate of the population​ mean,

.A study of 100 patients with back pain reported that the mean duration of pain was 12 months. It is known that the standard deviation of duration of back pain is 6.8 months. Assuming that the duration of this problem is normally distributed in the population; determine a 95% confidence interval for the mean duration of back pain in the population.

You are a data analyst for a health insurance company and want to estimate the population mean of the surgery durations for all heart valve patients. To do so, you select a random sample of 32 heart valve surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all heart valve surgeries is 1.92 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 heart valve patients. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 32 heart valve patients. (b) Take Sample Sample size: 0 Point estimate: 0 Population standard deviation: 0 Critical value: 0 Compute 0.00 0.00 Number of patients 32 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%…

For a confidence level of 94%, find the critical value for a confidence interval on a one sample proportion.