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Description: Two treatments for a new infectious disease have been developed to reduce hospitalizations. Each treatment was given to different groups of patients. Treatment 1 was given to n1 = 56 people. Subjects of treatment 1 had a mean hospital stay of x1 = 5.

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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Two treatments for a new infectious disease have been developed to reduce hospitalizations. Each treatment was given to different groups of patients. Treatment 1 was given to n1 = 56 people. Subjects of treatment 1 had a mean hospital stay of x1 = 5.4 days with a standard deviation of s1 = 2.7 days. Treatment 2 was given to n2 = 45 people.
Subjects of treatment 2 had a mean hospital stay of x2 = 8.8 days with a standard deviation of s2 = 3.1 days. Use the method of hypothesis testing to test the claim that the mean time in the hospital for treatment 1 is shorter than the mean time in the hospital for treatment 2 assuming a 0.01 significance level
(a) List the null hypothesis H0 and the alternative hypothesis Ha for this test.
(b) Compute the value of the test statistic

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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