Answered: Q2 A study was conducted to test 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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Q2 A study was conducted to test the effect of melatonin on female dementia patients. A random sample of 10 patients was given a dose of 2.5 mg of melatonin daily, while a control group of 10 patients was given a placebo. The data below are the subjective well-being scores for each of the patients after two months on the assigned treatment. Higher scores indicate greater well-being. Is there a difference in mean well-being score between the two treatments? Assume Equal Variances. Run the test at a 5% level of significance.  1 ) the appropriate null and alternative hypotheses ( 2) the appropriate test ); 3) the decision rule ; 4) the calculation of the test statistic, 5) your conclusion including a comparison to alpha or the critical value, What do the results mean?

Melatonin
21
16
13
18
18
15
10
16
12
17
Placebo
15
12
11
13
12
7
10
13
14
9

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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