Following is an incomplete ANOVA table. ANOVA Sum of Squares df Mean Square F Be
ID: 2949874 • Letter: F
Question
Following is an incomplete ANOVA table.
ANOVA
Sum of Squares
df
Mean Square
F
Between Groups
30
3
Within Groups
8
XXXXXX
Total
52
11
XXXXXX
XXXXXX
Enter the F-test statistic value with three decimal places (#.###) _______
Question 20 options:
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Question 21 (1 point)
How many groups were in the study?
Question 21 options:
2
3
4
8
9
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Question 22 (1 point)
Assuming equal group sizes, how many subjects were in each group?
Question 22 options:
2
3
4
8
9
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Question 23 (1 point)
Which of the following is the conclusion from the data results, using a .05 level of significance?
Question 23 options:
All group means are equal.
All group means are significantly different.
At least one group mean is significantly different from the others.
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Question 24 (1 point)
A catalogue randomly selects 125 subscribers, of whom 105 are women and 20 are men. Of the women, 65 regularly place an order; of the men, 15 regularly place an order. Which of the following is closest to the expected number of women who place an order?
Question 24 options:
38
40
67
80
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Question 25 (1 point)
Coin comes up heads 65 times and tails 35 times. What is the computed chi-square value for the ?2{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>χ</mi><mn>2</mn></msup></math>"} goodness-of-fit test that assumes an equal number of heads and tails. Enter the value with three decimal places (#.###): _______
ANOVA
Sum of Squares
df
Mean Square
F
Between Groups
30
3
Within Groups
8
XXXXXX
Total
52
11
XXXXXX
XXXXXX
Explanation / Answer
Solution:
Required ANOVA table is given as below:
Sum of square for within groups = total sum of squares - between sum of squares
Sum of square for within groups = 52 – 30 = 22
Mean square = Sum of square / df
F = MSB/MSW
df1 = 3, df2 = 8
ANOVA
S.V.
Sum of squares
df
Mean Square
F
P-value
F-critical
Between groups
30
3
10
3.636364
0.064046
4.066181
Within groups
22
8
2.75
Total
52
11
[P-value, and F-critical values are calculated by using F-table or excel.]
[Excel commands: =Fdist(F,df1,df2) and Finv(?,df1,df2)]
Question 20
F-test statistic = 3.636
Question 21
How many groups were in the study?
Answer: 4
(...because df for between groups is 3, so total number of groups is 3+1 = 4)
Question 22
Assuming equal group sizes, how many subjects were in each group?
Total number of groups = 4
Total number of subjects = 11+1 = 12
(...because df for total is 11, so total 11+1 = 12 number of subjects)
Each groups is of equal size, so
Group size = 12/4 = 3
Answer: 3
Question 23
Which of the following is the conclusion from the data results, using a .05 level of significance?
We have
P-value = 0.064046
? = 0.05
P-value > ?
So, we do not reject the null hypothesis that all group means are equal.
Answer:
All group means are equal.
Question 24
A catalogue randomly selects 125 subscribers, of whom 105 are women and 20 are men. Of the women, 65 regularly place an order; of the men, 15 regularly place an order. Which of the following is closest to the expected number of women who place an order?
Total number of subscribers = n = 125
Number of women place an order = 65
So, number 67 is closest to the expected number of women who place an order.
Answer: 67
ANOVA
S.V.
Sum of squares
df
Mean Square
F
P-value
F-critical
Between groups
30
3
10
3.636364
0.064046
4.066181
Within groups
22
8
2.75
Total
52
11