Answered: hospital in New York commonly conducts…

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

A hospital in New York commonly conducts stress tests to study the heart muscle after a person has a heart attack. Members of the diagnostic imaging department conducted a quality improvement project with the objective of reducing the turnaround time for stress tests. Turnaround time is defined as the time from when a test is ordered to when the radiologist signs off on the test results. Initially, the mean turnaround time for a stress test was 68 hours. After incorporating changes into the stress-test process, the quality improvement team collected a sample of 50 turnaround times. In this sample, the mean turnaround time was 32 hours, with a sample standard deviation of 9 hours.

(a) Using the critical value approach, if you test the null hypothesis at the 0.01 level of significance, is there evidence that the new process has reduced turnaround time? (Be sure to list the null and alternate hypotheses, the value of the test statistic, the decision rule (using the critical value(s) and conclude in a complete sentence including why you made the decision you did in terms of the decision rule.)

(b) Using the p-value approach, if you test the null hypothesis at the 0.01 level of significance, is there evidence that the new process has reduced turnaround time? (You’ve already listed the null and alternate hypotheses and value of the test statistic in part (a). For part (b), include the p-value, the decision rule (using the p-value) and conclusion in a complete sentence including why you made the decision you did in terms of the decision rule.)

(c) Compare your conclusions in (a) and (b). Was it the same or different? Do you expect this to always or only sometimes be the case?

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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