a) Write down the null and the alternative hypothesis of the ANOVA test. b) What is the F-test statistic value of the test? Explain whether the null hypothesis should be rejected in this ANOVA test. c) Based on the Post Hoc Test result, fill in “<”, “>” or “=” for the following comparisons by using a 5% significance level. (i) ?1 _____ ?2 (ii) ?1 _____ ?3 (iii) ?1 _____ ?4 (iv) ?2 _____ ?3 (v) ?2 _____ ?4 (vi) ?3 _____ ?4 d) With the results in (c), write a summary about the difference in the cholesterol levels of adults in different BMI categories.
a) Write down the null and the alternative hypothesis of the ANOVA test. b) What is the F-test statistic value of the test? Explain whether the null hypothesis should be rejected in this ANOVA test. c) Based on the Post Hoc Test result, fill in “<”, “>” or “=” for the following comparisons by using a 5% significance level. (i) ?1 _____ ?2 (ii) ?1 _____ ?3 (iii) ?1 _____ ?4 (iv) ?2 _____ ?3 (v) ?2 _____ ?4 (vi) ?3 _____ ?4 d) With the results in (c), write a summary about the difference in the cholesterol levels of adults in different BMI categories.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
a) Write down the null and the alternative hypothesis of the ANOVA test.
b) What is the F-test statistic value of the test? Explain whether the null hypothesis should be rejected in this ANOVA test.
c) Based on the Post Hoc Test result, fill in “<”, “>” or “=” for the following comparisons
by using a 5% significance level.
(i) ?1 _____ ?2 (ii) ?1 _____ ?3 (iii) ?1 _____ ?4 (iv) ?2 _____ ?3 (v) ?2 _____ ?4 (vi) ?3 _____ ?4
d) With the results in (c), write a summary about the difference in the cholesterol levels of
adults in different BMI categories.
Transcribed Image Text:Post Hoc Tests
Dependent Variable: Cholesterol level
Bonferroni
(1) BMI Category (J) BMI Category
Underweight
Normal
Overweight
Obese
Normal
Overweight
Underweight
Overweight
Obese
Obese
Multiple Comparisons
Mean
Difference (1-
J)
Underweight
Normal
Obese
-8.592
Underweight
34.976*
Normal
21.976*
Overweight
8.592
*. The mean difference is significant at the 0.05 level.
-13.000*
-26.384*
-34.976*
13.000*
-13.384*
-21.976*
26.384*
13.384*
Std. Error
4.731
4.944
5.637
4.731
4.686
5.412
4.944
4.686
5.599
5.637
5.412
5.599
Sig.
.042
.000
.000
.042
.031
.001
.000
.031
.767
.000
.001
.767
95% Confidence Interval
Lower Bound Upper Bound
-25.72
-.28
-39.68
-13.09
-50.13
-19.82
25.72
-.79
-7.42
39.68
25.98
6.46
50.13
36.53
23.65
.28
-25.98
-36.53
13.09
.79
-23.65
19.82
7.42
-6.46
Transcribed Image Text:A research is performed to compare the cholesterol levels of adults in different BMI categories.
The four BMI categories are "underweight", "normal weight", "overweight" and "obese". A
sample of 110 adults is obtained. They are classified into different BMI categories and their
cholesterol levels are recorded.
Let
μ₁ = the population mean cholesterol level of underweight adults;
M₂ = the population mean cholesterol level of normal weight adults;
μ3 = the population mean cholesterol level of overweight adults; and
M4 = the population mean cholesterol level of obese adults.
The ANOVA table and the Post Hoc Test results are shown below (with some information
hidden):
Cholesterol level
Between Groups
Within Groups
Total
Post Hoc Tests
Sum of
Squares
17018.694
36909.525
53928.218
ANOVA
df
109
Mean Square
F
Sig.
.000
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