In a science competition between two states, 20 students from each state were selected for the final stage. These students were given the same mathematics, chemistry, and English exams at the same time and under the same conditions. 4 marks for each exam from each state were randomly selected from each of the groups of 20 students, and recorded in the following table: State 1 State 2 Mathematics 98.6 74.2 79.0 94.7 88.6 90.7 90.8 89.6 Chemistry 78.6 88.4 82.1 93.1 93.6 84.2 88.9 96.0 English 92.8 88.9 85.6 83.6 98.4 96.0 78.4 91.1 a) Find summary statistics for the exam marks, across both States, Subjects, and the combination of both variables using the statistical package of your choice. b) Perform a two-way ANOVA to investigate the effect of State and Subject on exam marks and write the conclusion. Plot the interaction if it exists.

In a science competition between two states, 20 students from each state were selected for the final stage. These students were given the same mathematics, chemistry, and English exams at the same time and under the same conditions. 4 marks for each exam from each state were randomly selected from each of the groups of 20 students, and recorded in the following table: State 1 State 2 Mathematics 98.6 74.2 79.0 94.7 88.6 90.7 90.8 89.6 Chemistry 78.6 88.4 82.1 93.1 93.6 84.2 88.9 96.0 English 92.8 88.9 85.6 83.6 98.4 96.0 78.4 91.1 a) Find summary statistics for the exam marks, across both States, Subjects, and the combination of both variables using the statistical package of your choice. b) Perform a two-way ANOVA to investigate the effect of State and Subject on exam marks and write the conclusion. Plot the interaction if it exists.

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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Question

In a science competition between two states, 20 students from each state were selected for
the final stage. These students were given the same mathematics, chemistry, and English
exams at the same time and under the same conditions. 4 marks for each exam from each
state were randomly selected from each of the groups of 20 students, and recorded in the
following table:
State 1
State 2
Mathematics
98.6
74.2
79.0
94.7
88.6
90.7
90.8
89.6
Chemistry
78.6
88.4
82.1
93.1
93.6
84.2
88.9
96.0
English
92.8
88.9
85.6
83.6
98.4
96.0
78.4
91.1
a) Find summary statistics for the exam marks, across both States, Subjects, and
the combination of both variables using the statistical package of your choice.
b) Perform a two-way ANOVA to investigate the effect of State and
Subject on exam marks and write the conclusion. Plot the interaction if it exists.

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Follow-up Question

c) Write down the contrasts (calculate by hand, or use the statistical package of your choice)
and their related hypotheses for the following comparisons:
(i)
(ii)
(iii)
Compare mathematics-state A with mathematics-state B.
Compare mathematics-state A with the average of Chemistry and English-
state A.
Compare the average of mathematics States A and B with the average of
English States A and B.
d) Use Tukey's HSD comparison (where appropriate) to conduct post-hoc testing for the two-
way
ANOVA conducted in part b of this question and write your conclusion. Add appropriate
plots.

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