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Using the latest in medical technology, an orthopedic doctor has developed a new surgical procedure that he believes is an improvement over the standard procedure. He wants to study whether the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who have the standard procedure, The doctor studies a random sample of il patients who have the new procedure and a random sample of 9 patients who have the standard procedure. (These samples are chosen independently.) The doctor records each patient's recovery time (in days). The patients who had the new procedure have a sample mean recovery time of 380.4 with a sample variance of 3189.7. The patients who had the standard procedure have a sample mean recovery time of 424.8 with a sample variance of 469.2 Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.05 level of significance, that the population mean of the recovery times of patients who have the new procedure is less than the population mean of recovery times of patients who have the standard procedure? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consulta list of formulas) (a) State the null hypothesis and the alternate hypothesis 1 0 P 1:0 X yo Da (1) Determine the type of test statistic to use (Choose one) C- O DO DO (c) Find the value of the test statistic (Round to three or more decimal placou.) 0 Continue Save For Later Sunt Assig

IX $ co Dla DO OSO 020 , H:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) DO < > x х 6 2 (e) At the 0.05 level of significance, can the doctor conclude that the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who have the standard procedure? Yes No