You are interested in finding a 95% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 13 randomly selected physical therapy patients. Round answers to 3 decimal places where possible. 17 8 9 26 27 11 25 10 7 15 19 a. To compute the confidence interval use a ? distribution. b. With 95% confidence the population mean number of visits per physical therapy patient is between and visits. c. If many groups of 13 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per patient and about percent will not contain the true population mean number of visits per patient.

a. Since the population standard deviation is unknown, t distribution can be used for the computation of confidence interval.b. Sample mean and standard deviation: Enter the values in columns A of an excel. The sample mean is 14.23 (using the Excel function, =AVERAGE(A1:A13). The sample standard deviation is 7.90 (using the Excel function, =STDEV.S(A1:A13)). The sample mean = 14.23. Sample standard deviation, s is 7.90. The sample size, n is 13. The degrees of freedom is 13-1 =12. From the EXCEL, using the formula, =T.INV.2T(0.05,12), the critical value is 2.179. The margin of error is calculated as follows: Margin of error = t×(s/√n) = 2.179×(7.90/√13) = 4.774 The 95% confidence interval is given by: CI = point estimate ±Margin of error = 14.23 ± 4.774 = (9.456, 19.004) With 95% confidence the population mean number of visits per physical therapy patient is between 9.456 and 19.004 visits. c. If many groups of 13 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population mean number of visits per patient and about 5 percent will not contain the true population mean number of visits per patient.