Answered: The following data are from a study on…

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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(OPHTHALMOLOGY) The following data are from a study on Botox injections. Patients received a high-dose injection in one eye (experimental treatment = treatment E) and a low-dose injection in the other eye (control treatment = treatment C). Patients were asked to rate the level of pain in each eye on a 1–10 scale, with higher scores indicating more pain. The assignment of treatments to eyes was randomized. The subjects came back over several visits. Data from the last visit are given in the following table:

1. Which of the following is the correct test to conduct given the situation above?

2. The hypotheses are:

3. What is the level of significance?

4. What is the computed test statistic? Hint: Use (mean of "Pain in E eye") minus (mean of "Pain in C eye")

5. What is the correct decision based on the p-value or critical value method?

Effect of Botox injection on eye pain
Pain score at the last visit
Subject
Pain in E eye
Pain in C eye
1
1.3
8.8
2
7.3
1.3
3
0.8
4
9.5
7.8
9.0
7
3.5
5.0
8
2.3
2.5
10
2.0
8.0
11
4.5
12
3.0
4.5
13
5.0
9.0
14
0.3
7.5
15
0.5
16
0.8
4.3
Perform the appropriate t-test and identify whether there is a significant difference
between the means of the two data sets.

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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