Answered: A medical researcher examined 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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A medical researcher examined the number of asthma attacks patients had both before and while using an advanced air purifier. Seven patients were included in the study. The number of asthma attacks for each patient before and during using the air purifier is reported below. Use α = .05, 2-tailed.

Patient	Before Purifier	During Purifier
1	6	4
2	9	7
3	11	5
4	6	4
5	7	3
6	9	6
7	5	4

a.State the null and alternative hypotheses below.

b.What type of test should be run on the data (be specific with the exact name of the test)? For example, don’t just state “t test,” but the specific t test used.

c.What is the conclusion of the hypothesis test? State the p-value and the decision about the hypothesis test below. (Don’t write the results here – that will be done in (e) below – just state p and whether H₀ is rejected.)

d.What is the effect size for the study? (1) Calculate and report the effect size below. (2) Indicate the magnitude of the effect size according to Cohen’s standards and (3) interpret what the effect size means in terms of standard deviation units.

e.Write the results of the test in APA format below. (Hint: This type of write-up would be structured in a similar fashion to what you see in your text.)

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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