Answered: State the null hypothesis H0 and the…

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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Medical researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic mental illness established two independent test groups. The first group consisted of 8 people with the illness, and the second group consisted of 14 people with the illness. The first group received treatment 1 and had a mean time until remission of 163 days, with a standard deviation of 9 days. The second group received treatment 2 and had a mean time until remission of 174 days, with a standard deviation of 8 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.05 level of significance, that the mean number of days before remission after treatment 1, μ1, differs from the mean number of days before remission after treatment 2, μ2? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

a. State the null hypothesis H0 and the alternative hypothesis H1.

b. Find the value of the test statistic. Round to three or more decimal places.

c. Find the p-value. Round to three or more decimal places.

d. Can we conclude that the mean number of days before remission after treatment 1 differs from the mean number of days before remission after treatment 2?

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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