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 11 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). These data are shown in the table. New procedure Standard procedure Send data to calculator Recovery times (in days) 347, 265, 380, 325, 317, 289, 410, 323, 294, 297, 275 343, 345, 362, 361, 373, 363, 328, 310, 366 Send data to Excel Calculato Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 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, consult a list of formulas.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

1. Find the p-value. (Round to three or more decimal places.)

2. At the 0.01 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?

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 11 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). These data are shown in the table.
Recovery times (in days)
New procedure 347, 265, 380, 325, 317, 289, 410, 323, 294, 297, 275
Standard procedure 343, 345, 362, 361, 373, 363, 328, 310, 366
Send data to calculator V
Send data to Excel
Calculator
Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 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, consult a list of formulas.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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