When only two treatments are involved, ANOVA and the Student’s t test (Chapter 1
ID: 3227582 • Letter: W
Question
When only two treatments are involved, ANOVA and the Student’s t test (Chapter 11) result in the same conclusions. Also, formula120.mml. As an example, 14 randomly selected Introduction to History students were divided into two groups, one consisting of 6 students and the other of 8. One group took the course in the normal lecture format. The other group of 8 students took the course via the Internet. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups.
Traditional Lecture Internet 16 35 13 23 24 39 26 25 14 25 14 24 25 24
Value: 10.00 points When only two treatments are involved, ANOVA and the Student's t test (Chapter 11) result in the same conclusions. Also, t F. As an example, 14 randomly selected Introduction to History students were divided into two groups, one consisting of 6 students and the other of 8. One group took the course in the normal lecture format. The other group of 8 students took the course via the Internet. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups Traditional Lecture Internet 16 35 13 23 39 24 26 25 14 25 14 24 25 24 a-1. Complete the ANOVA table. (Round SS, MS and F values to 2 decimal places.) df MS Source Factors 12 Error 13 Total a-2. Use a a 0.1 level of significance. (Round your answer to 2 decimal places.) The test statistic is F b. Using the t test from Chapter 11, compute t. Negative amount should be indicated by a minus sign Round your answer to 2 decimal places.) c. There is is no difference n the mean test scores.Explanation / Answer
Answer:
A1).
ANOVA table
Source
SS
df
MS
F
Treatment
320.38
1
320.38
9.31
Error
412.83
12
34.40
Total
733.21
13
Test statistic F= 9.31
a2).
t= -3.05
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
6
Sample Mean
17.8333
Sample Standard Deviation
5.6716
Population 2 Sample
Sample Size
8
Sample Mean
27.5
Sample Standard Deviation
6
Intermediate Calculations
Population 1 Sample Degrees of Freedom
5
Population 2 Sample Degrees of Freedom
7
Total Degrees of Freedom
12
Pooled Variance
34.4028
Standard Error
3.1677
Difference in Sample Means
-9.6667
t Test Statistic
-3.0517
Two-Tail Test
Lower Critical Value
-2.1788
Upper Critical Value
2.1788
p-Value
0.0101
Reject the null hypothesis
c. There is significant difference in the mean test scores.
ANOVA table
Source
SS
df
MS
F
Treatment
320.38
1
320.38
9.31
Error
412.83
12
34.40
Total
733.21
13
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