A professor gives an exam to a class with four recitation sections. Each section has 7 students. The professor has no reason to assume that the exam scores would not be independent and normally distributed with equal variance. However, it is unknown whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test. The professor conducts a one-way ANOVA, and finds that Ho should be rejected at a significance level of a = 0.01.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 27PPS
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Please explain and fill table with steps by step results 

Comparison Groups
Groups
(ascending order) Group A
Group B
Group C
Group D
Group A = 3
Group B = 4
Group C = 2
Group D = 1
Transcribed Image Text:Comparison Groups Groups (ascending order) Group A Group B Group C Group D Group A = 3 Group B = 4 Group C = 2 Group D = 1
A professor gives an exam to a class with four recitation sections. Each section has 7 students. The professor
has no reason to assume that the exam scores would not be independent and normally distributed with equal
variance. However, it is unknown whether or not the section choice (different TAs and different days of the
week) has any relationship with how students performed on the test. The professor conducts a one-way
ANOVA, and finds that Ho should be rejected at a significance level of a =
0.01.
Source
SS
df
MS
F-ratio P-value
Between
1889.293 3 629.764
5.257
0.0062
Within
2875.271 24 119.803
As shown above, the professor finds that F(3,24)
5.257, which has a probability of
0.0062 of
occurring randomly. Additionally, the error variance was estimated as MSw
means for each group were obtained as shown in the table below.
119.803, and the sample
Level
Mean
Group-1
88.214
Group-2
Group-3
Group-4
87.657
69.314
74.557
The professor decides to use the Tukey HSD method to test all possible pairwise contrasts. To do so, the
following table of q; statistics needs to be completed. For this presentation, the groups will be ordered from
smallest to largest means. (In other words, Group A should be the group with the smallest mean.) First,
indicate the appropriate order for the groups (use the group number). Then fill in the table with values
rounded to 3 decimal places. (Furthermore, even though the sign does not matter, report all comparison
statistics as positive values.)
(Note: we often create a table
statistics, which we will compare to qcritical)
differences an
compare those to HSD. In th
case, we need a table of a
Transcribed Image Text:A professor gives an exam to a class with four recitation sections. Each section has 7 students. The professor has no reason to assume that the exam scores would not be independent and normally distributed with equal variance. However, it is unknown whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test. The professor conducts a one-way ANOVA, and finds that Ho should be rejected at a significance level of a = 0.01. Source SS df MS F-ratio P-value Between 1889.293 3 629.764 5.257 0.0062 Within 2875.271 24 119.803 As shown above, the professor finds that F(3,24) 5.257, which has a probability of 0.0062 of occurring randomly. Additionally, the error variance was estimated as MSw means for each group were obtained as shown in the table below. 119.803, and the sample Level Mean Group-1 88.214 Group-2 Group-3 Group-4 87.657 69.314 74.557 The professor decides to use the Tukey HSD method to test all possible pairwise contrasts. To do so, the following table of q; statistics needs to be completed. For this presentation, the groups will be ordered from smallest to largest means. (In other words, Group A should be the group with the smallest mean.) First, indicate the appropriate order for the groups (use the group number). Then fill in the table with values rounded to 3 decimal places. (Furthermore, even though the sign does not matter, report all comparison statistics as positive values.) (Note: we often create a table statistics, which we will compare to qcritical) differences an compare those to HSD. In th case, we need a table of a
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