# Practice Questions 8.3

1. For the ANOVA method, select all choices below that are assumptions of this method.

A. Individuals are chosen randomly from each population.
B. Each data value is independent of all other data values.
C. Each population has the normal shape.
D. All populations have the same variance.
A, B, C, and D
2. With a computer, which statistical method is used to find out if the shape of a population is normal?

A.
3. Using the computer output below, should this population be considered to have the normal shape?
Goodness-of-Fit Test
W Prob<W
Shapiro-Wilk 0.9186235 0.4188

D.
4. With a computer, which statistical method is used to find out if all the populations have the same variance?

D.
5. Using the computer output below, is it appropriate to consider that all populations have the same variance?
Test F Ratio DFNum DFDen Prob > F
O'Brien[.5] 1.4419 2 21 0.2590
Brown-Forsythe 1.1006 2 D21 0.3511
Levene 1.3125 2 D21 0.2903
Bartlett 0.4683 2 . 0.6261

A.
6. The two variances of the ANOVA fraction are shown below, what two variances are used in the ANOVA table?
(s²x) and (s²pooled / n)

A.
7. For the ANOVA table, select all choices that is a column heading in the ANOVA table.

A. Source column.
B. Degrees of Freedom column.
C. Sum-of-Squares column
D. Mean Squares column.
E. F-Value column.
F. P-Value column.
All
8. In the ANOVA table below, are all the degrees of freedom correct if there are three (3) populations and ten (10) data values from each population?

Analysis of Variance
Source DF Sum of Square Mean Square F Ratio Prob> F
Day 2 7129434 3564717 18.3965 <.0001*
21 21 4069197 193771
C. Total 23 11198631

A.

• n_total= 3 x 10 = 30
• Therefore, C. Total should be 30.

For Error: 30-3= 27
9. In the ANOVA table below, what is the value of the F-Ratio.

Analysis of Variance
Source DF Sum of Squares Mean Square F Ratio Prob> F
Day 2 7129434 3566717 jQuery1124037259809705227087_1712104222390? <.0001*
Error 21 4069197 196771
C. Total 2311198631

C.

• F-ratio= MS Day / MS Error
• = 3566717 / 196771
• =18.1262
10. In the ANOVA table below, match up the values of the two Mean Squares.

Analysis of Variance
Sourec DF Sum of Squares Mean Square F Ratio Prob> F
DAY 2 7121434 jQuery1124018545071294071036_1712455621884? 18.3965 <.0001*
Error 21 4062197 jQuery112404324943061533939_1712455744412?
C. Total 23 11183631

A. MS(Errpr)
B. MS(DAY)

__ 3,560,717
__ 193,437
• B
• A

To find MS Day and MS Error, just do: Sum of squares / DF

• = 7121434/2
• = 3,560,717

• = 4062197/21
• =193,437
11. In the ANOVA table below, match up the values of the two Sum of Squares.

Analysis of Variance
Sourec DF Sum of Squares Mean Square F Ratio Prob> F
DAY 2 jQuery112401157404587023958_1712521158377? 3564717 18.3965 <.0001*
Error 21 jQuery112406352651159208165_1712527155458? 193771
C. Total 23 11183631

A. SS(Error)
B. SS{DAY}

__ 7,129,434
__ 4,069,197
• B
• A

To get Sum of Squares just do: MS x DF

• = 3564717 x 2
• 7,129,434

• 193771 x 21
• = 4,069,197
12. In the ANOVA table below, should the populations means be considered equal?

Analysis of Variance
Sourec DF Sum of Squares Mean Square F Ratio Prob> F
DAY 2 7129434 3564717 18.3965 <.0001*
Error 21 4069197 193771
C. Total 23 11183631

B.

• The only thing that matters is the Prob> F section.
• Because it is smaller than 0.05, we reject it. This means it is not equal.
13. In the ANOVA table below, should the populations variances be considered equal?

C.

The table tells us nothing about the variances.
14. Please match each table below with its purpose in the ANOVA method.

A. The Tukey table
B. The ANOVA table

__ Gives an overall test to tell if all population means are equal.
__ Gives a series of tests to tell which population means are equal.
• B
• A
15. Does the Tukey table provide new information when the null hypothesis is not rejected in the ANOVA table?

B.
16. Does the Tukey table provide new information when the null hypothesis is rejected in the ANOVA table

A.
17. In the Tukey table shown below from a study of the number of births per weekday, what relationship between the values of the population means is NOT appropriate?

Tukey Table
Connecting Letters Report
Level Mean
FRIDAY A 12002.875
WEDNESDAY A 11586.875
MONDAY B 10696.250

A.
18. In the Tukey table shown below from a study of the number of births per weekday, what relationship between the values of the population means is appropriate?

Tukey Table
Connecting Letters Report
Level Mean
TUESDAYA 12237.125
THURSDAYA 11897.875
WEDNESDAYA 11586.875
• A. Tuesday's, Thursday's, and Wednesday's population mean number of births are all equal.
• B. Tuesday's and Thursday's population number of births are both greater than Wednesday's population mean.
• C. None of the population mean number of births are equal.
• D. Tuesday's population mean number of births = Thursdays ≠ Wednesday's.
19. Given the information shown below from a study of the number of births per weekday, please match each of the following questions with their appropriate answers.

A. Which population means are equal / not equal.
B. Is the assumption of equal population variances met?
C. Is the assumption of Normality met?
D. Are all population means equal?

__ Yes, because all SW p-values are greater than 0.05.
__ Yes, because Levene' p-value is greater than 0.05.
__ No, because the ANOVA p-value is less than 0.05.
__ Friday & Wednesday are equal / not Monday.
• C,
• B
• D
• A

A) Use the Tukey Table: If any two have the same letter, they are considered equal. So, Friday and Wednesday are equal.

B) Use Levene's Test: If the final value in "Prob>F" is greater than 0.05 then yes.

C) Depends on the Shapiro-Wilks Test: If all values are >0.05 then yes.

D) Depends on the ANOVA p-value found in the Analysis of Variance table: Because last value is less than 0.05, it's no.
20. Given the information shown below from a study of the number of births per weekday, please match each of the following questions with their appropriate answers.

A. Which population means are equal / not equal.
B. Are all population means equal?
C. Is the assumption of equal population variances met?
D. Is the assumption of Normality met?

__ Yes, because all SW p-values are greater than 0.05
__ Yes, because Levene' p-value is greater than 0.05
__ Yes, because the ANOVA p-value is greater than 0.05.
__ Tuesday = Wednesday = Thursday, because all days have the same Tukey letter.
• B,
• D
• C
• A

A) Tukey Table: Tuesday, Wednesday, and Thursday are all equal because they have the same letter.

B) ANOVA value in Analysis of Variance table: Yes, because value greater than 0.05

C) Levenes Test: Yes, because all values greater than 0.05.

D) Shapiro-Wilks Test: Yes, because all values greater than 0.05.
21. Given the information shown below from a study of the number of births by season, please match each of the following questions with their appropriate answers.

A. Is the assumption of Normality met?
B. Which population means are equal / not equal.
C. Are all population means equal?
D. Is the assumption of equal population variances met?

__ No, SW indicates that Winter and Summer do not have the normal shape.
__ Yes, because Levene' p-value is greater than 0.05.
__ Yes, because the ANOVA p-value is greater than 0.05.
__ Tukey's table does not add any new information.
• A,
• D
• C
• B

A) Shapiro-Wilks Test: No, not all values are greater than 0.05.

B) Tukey Table: Tukey table does not add any new information since we know all the population means are equal.

C) ANOVA in Analysis of Variance: Yes, because it is greater than 0.05.

D) Levene's Test: Yes, because all values are greater than
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Practice Questions 8.3
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