You may need to use the appropriate technology to answer this question. Information regarding the ACT scores of samples of students in three different majors is given below. Sample Size Average Major Management Finance Accounting 12 Within Treatments Total 26 Sample Variance (a) Compute the overall sample mean . 29.5 x 17 9 23 6 11 25. (b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your F statistic to two decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square Between Treatments 11 (c) Using a = 0.01, determine the critical value of F. (Round your answer to two decimal places.) F

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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You may need to use the appropriate technology to answer this question.
Information regarding the ACT scores of samples of students in three different majors is given below.
12
esc
Sample Size
68°F
Clear
Average
Sample Variance
f1
(a) Compute the overall sample mean .
29.5
X
?
Management
Source of Variation
Between Treatments
Within Treatments
Total
2
12
*1
26
(b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your F statistic to two decimal places.)
17
*
#
3
Major
Finance
N
*****
9
23
Sum of Squares
$
4
6
(c) Using a = 0.01, determine the critical value of F. (Round your answer to two decimal places.)
(d) Using the critical value approach, test to determine whether there is a significant difference in the means of the three populations.
We should not reject Ho and therefore can conclude that there is a significant difference among the means of the three populations.
We should not reject H. and therefore cannot conclude that there is a significant difference among the means of the three
populations.
We should reject H, and therefore cannot conclude that there is a significant difference among the means of the three populations.
We should reject H. and therefore can conclude that there is a significant difference among the means of the three populations.
O
Accounting
f5
11
%
25
Degrees of Freedom
5
11
f6
4-
6
Mean Square
F
4+
&
7
fg
IAA
19
F
DII
hp
f10
9
112
insert
NA
prt sc
11
W
delete
backspace
home
2
num
lock
CATE
end
9:15 PM
10/16/2022
*1
*****
TICO
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Transcribed Image Text:You may need to use the appropriate technology to answer this question. Information regarding the ACT scores of samples of students in three different majors is given below. 12 esc Sample Size 68°F Clear Average Sample Variance f1 (a) Compute the overall sample mean . 29.5 X ? Management Source of Variation Between Treatments Within Treatments Total 2 12 *1 26 (b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your F statistic to two decimal places.) 17 * # 3 Major Finance N ***** 9 23 Sum of Squares $ 4 6 (c) Using a = 0.01, determine the critical value of F. (Round your answer to two decimal places.) (d) Using the critical value approach, test to determine whether there is a significant difference in the means of the three populations. We should not reject Ho and therefore can conclude that there is a significant difference among the means of the three populations. We should not reject H. and therefore cannot conclude that there is a significant difference among the means of the three populations. We should reject H, and therefore cannot conclude that there is a significant difference among the means of the three populations. We should reject H. and therefore can conclude that there is a significant difference among the means of the three populations. O Accounting f5 11 % 25 Degrees of Freedom 5 11 f6 4- 6 Mean Square F 4+ & 7 fg IAA 19 F DII hp f10 9 112 insert NA prt sc 11 W delete backspace home 2 num lock CATE end 9:15 PM 10/16/2022 *1 ***** TICO pg up 3 pg dn
(a) Compute the overall sample mean .
29.5
X
esc
K-
(b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your F statistic to two decimal places.)
68°F
Clear
Source of Variation Sum of Squares Degrees of Freedom
Between Treatments
Within Treatments
?
(c) Using a = 0.01, determine the critical value of F. (Round your answer to two decimal places.)
Total
(d) Using the critical value approach, test to determine whether there is a significant difference in the means of the three populations.
O We should not reject H. and therefore can conclude that there is a significant difference among the means of the three populations.
We should not reject Ho and therefore cannot conclude that there is a significant difference among the means of the three
populations.
O We should reject Ho and therefore cannot conclude that there is a significant difference among the means of the three populations.
O We should reject H. and therefore can conclude that there is a significant difference among the means of the three populations.
Need Help? Read it
(e) Determine the p-value and use it for the test. (Round your answer to three decimal places.)
The p-value =
Since this is greater than
difference among the mean ACT scores of the three majors,
f2
@
2
f3
14/
#
*
3
ALE
14
11
$
4
%
5
T
Mean Square
6
&
the significance level we should not ✔✔✔ reject Ho and conclude that there is not
7
fa
144
8
F
DI
10
fio
DDI
O
0
(12
Insert
{
prt sc
[
W
G
sufficient evidence in the data to suggest a significant
NE
delete
backspace
home
num
lock
end
9:16 PM
10/16/2022
pg up
8
> 00
pg dn
4
Transcribed Image Text:(a) Compute the overall sample mean . 29.5 X esc K- (b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your F statistic to two decimal places.) 68°F Clear Source of Variation Sum of Squares Degrees of Freedom Between Treatments Within Treatments ? (c) Using a = 0.01, determine the critical value of F. (Round your answer to two decimal places.) Total (d) Using the critical value approach, test to determine whether there is a significant difference in the means of the three populations. O We should not reject H. and therefore can conclude that there is a significant difference among the means of the three populations. We should not reject Ho and therefore cannot conclude that there is a significant difference among the means of the three populations. O We should reject Ho and therefore cannot conclude that there is a significant difference among the means of the three populations. O We should reject H. and therefore can conclude that there is a significant difference among the means of the three populations. Need Help? Read it (e) Determine the p-value and use it for the test. (Round your answer to three decimal places.) The p-value = Since this is greater than difference among the mean ACT scores of the three majors, f2 @ 2 f3 14/ # * 3 ALE 14 11 $ 4 % 5 T Mean Square 6 & the significance level we should not ✔✔✔ reject Ho and conclude that there is not 7 fa 144 8 F DI 10 fio DDI O 0 (12 Insert { prt sc [ W G sufficient evidence in the data to suggest a significant NE delete backspace home num lock end 9:16 PM 10/16/2022 pg up 8 > 00 pg dn 4
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