A nationwide company specializing in preparing students for college and graduate school entrance exams, such as the SAT, ACT, and LSAT, had the business objective of improving its ACT preparatory course. Two factors of interest to the company are the length of the course (a condensed 10-day period or a regular 30-day period) and the type of course (traditional classroom or online distance learning). The company collected data by randomly assigning 10 clients to each of the four cells that represent a combination of length of the course and type of course. The results are organized and presented in the following table: LENGTH OF COURSE TYPE OF COURSE Condensed Regular Traditional 26 18 34 28 27 24 24 21 25 19 35 23 21 20 31 29 21 18 28 26 Online 27 21 24 21 29 32 16 19 30 20 22 19 24 28 20 24 30 29 23 25 The two-way ANOVA results are (Factor A (columns) is the lenght, factor B (sample) is the type of course) A B C D E F G 1 ANOVA: Two-ractor With Replication 2 3 SUMMARY Condensed Regular Total 4 traditional 5 Count 10 10 20 6 Sum 219 279 498 7 Average 8 Variance 21.9 27.9 24.9 11.2111 20.9889 24.7263 9 10 online 11 Count 10 10 20 12 Sum 270 213 483 13 Average 27 21.3 24.15 14 Variance 16.2222 8.0111 20.0289 15 16 Tulul 17 Count 20 20 18 Sum 189 192 19 Average 24.45 24.6 20 Variance 19.8395 25.2000 21 22 23 ANOVA 24 Source of Variation df 1 5.6250 0.3987 0.5318 4.1132 MS P-value r crit 25 Sample 5.6250 26 Columns 0.2250 1. 0.2250 0.0159 0.9002 4.1132 27 Interaction 342.2250 1 342.2250 24.2569 0.0000 4.1132 28 Within 507.9000 36 14.1083 29 30 Total 855.9750 39 31 Level of significance| 0.05 What are the effects of the type of course and the length of the course on ACT scores? To answer, at the 0.05 level of significance, (A) is there an interaction between the type of course and the length of the course? Answer: Since F=24.2560 > Fcrit, then we the null hypothesis.
A nationwide company specializing in preparing students for college and graduate school entrance exams, such as the SAT, ACT, and LSAT, had the business objective of improving its ACT preparatory course. Two factors of interest to the company are the length of the course (a condensed 10-day period or a regular 30-day period) and the type of course (traditional classroom or online distance learning). The company collected data by randomly assigning 10 clients to each of the four cells that represent a combination of length of the course and type of course. The results are organized and presented in the following table: LENGTH OF COURSE TYPE OF COURSE Condensed Regular Traditional 26 18 34 28 27 24 24 21 25 19 35 23 21 20 31 29 21 18 28 26 Online 27 21 24 21 29 32 16 19 30 20 22 19 24 28 20 24 30 29 23 25 The two-way ANOVA results are (Factor A (columns) is the lenght, factor B (sample) is the type of course) A B C D E F G 1 ANOVA: Two-ractor With Replication 2 3 SUMMARY Condensed Regular Total 4 traditional 5 Count 10 10 20 6 Sum 219 279 498 7 Average 8 Variance 21.9 27.9 24.9 11.2111 20.9889 24.7263 9 10 online 11 Count 10 10 20 12 Sum 270 213 483 13 Average 27 21.3 24.15 14 Variance 16.2222 8.0111 20.0289 15 16 Tulul 17 Count 20 20 18 Sum 189 192 19 Average 24.45 24.6 20 Variance 19.8395 25.2000 21 22 23 ANOVA 24 Source of Variation df 1 5.6250 0.3987 0.5318 4.1132 MS P-value r crit 25 Sample 5.6250 26 Columns 0.2250 1. 0.2250 0.0159 0.9002 4.1132 27 Interaction 342.2250 1 342.2250 24.2569 0.0000 4.1132 28 Within 507.9000 36 14.1083 29 30 Total 855.9750 39 31 Level of significance| 0.05 What are the effects of the type of course and the length of the course on ACT scores? To answer, at the 0.05 level of significance, (A) is there an interaction between the type of course and the length of the course? Answer: Since F=24.2560 > Fcrit, then we the null hypothesis.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.5: Interpreting Data
Problem 1C
Related questions
Topic Video
Question
Answer the blank space __________
(Question about the null hypothesis)
Transcribed Image Text:A nationwide company specializing in preparing students for college and graduate school entrance exams, such as the SAT, ACT, and
LSAT, had the business objective of improving its ACT preparatory course. Two factors of interest to the company are the length of
the course (a condensed 10-day period or a regular 30-day period) and the type of course (traditional classroom or online distance
learning). The company collected data by randomly assigning 10 clients to each of the four cells that represent a combination of
length of the course and type of course. The results are organized and presented in the following table:
LENGTH OF COURSE
TYPE OF COURSE
Condensed
Regular
Traditional
26 18
34 28
27 24
24 21
25 19
35 23
21 20
31 29
21 18
28 26
Online
27 21
24
21
29 32
16 19
30 20
22 19
24 28
20 24
30 29
23 25
The two-way ANOVA results are (Factor A (columns) is the lenght, factor B (sample) is the type of course )
A
B
1 ANOVA: Two-ractor With Replication
2
3 SUMMARY
Condensed Regular Total
4
traditional
5 Count
10
10
20
6 Sum
219
279
498
7 Average
21.9
27.9
24.9
8 Variance
11.2111 20.9889 24.7263
9
10
online
11 Count
10
10
20
12 Sum
270
213
483
13 Average
14 Variance
27
21.3
24.15
16.2222
8.0111 20.0289
15
16
Tulul
17 Count
20
20
18 Sum
189
192
19 Average
24.45
24.6
20 Variance
19.8395 25.2000
21
22
23 ANOVA
I crit
24 Source of Variation
25 Sample
26 Columns
df
MS
P-value
5.6250
5.6250 0.3987
0.5318 4.1132
0.2250
1
0.2250 0.0159
0.9002 4.1132
27 Interaction
342.2250
1 342.2250 24.2569
0.0000 4.1132
28 Within
507.9000
36 14.1083
29
30 Total
855.9750
39
31
Level of significance
0.05
What are the effects of the type of course and the length of the course on ACT scores?
To answer, at the 0.05 level of significance,
(A) is there an interaction between the type of course and the length of the course?
Answer: Since F=24.2560 > Fcrit, then we
the null hypothesis.
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