In the ANOVA table, what is the major meaning of the result shown below?
A. The ANOVA fraction = 0.28 . The sample averages are far enough apart implying the population means are different.
B. The Actual Variance and the Theoretical Variance do not have the same value.
C. This high a value for the ANOVA fraction indicates that all the population means have the same value.
D. The Actual Variance is 4.56 times the Theoretical Variance.
A.
How is the value of the Actual Variance found?A. By dividing the three sample variances by the square-root of n. B. By pooling the three sample variances. C. By averaging the three sample variances. D. By calculating the variance of the three sample averages.
D.
How is the value of the Theoretical Variance found?
A. By using the sampling distribution of the sample average
B. By getting the variance from the F-table and dividing by
√n
C. By using Levene's test to find out the value of the variances.
D. By calculating the pooled variance
(s²_pooled)
A.
What is the statistical importance of Pooling the variances?A. To combine the three variances into one value to make the calculations easier. B. Pooling gives a general consensus for the value of the population variance. C. Pooling is required to meet the needs of the equation. D. To combine three estimates of the population variance into one better estimate (it has more degrees of freedom).
D.
The ANOVA fraction gives a test statistic that follows what distribution?A. The F-distribution. B. The t-distribution. C. The A-distribution. D. The z-distribution.
A.
What does the F-distribution look like?A. Uni-modal and skewed to the left. B. Bi-modal and symmetrical. C. Uni-modal and skewed to the right. D. Non-modal and uniform.
C.
Use the information below to find the value of the Actual Variance.
Brand n x̄ s² A 9 5 9 B 9 10 10 C 9 15 11
A. Actual Variance = 25.
B. Actual Variance = 16.
C. Actual Variance = 10.
D. Actual Variance = 50.
A.
Find average: (5+10+15)/3= 10
Find (x-x̄): 5-10= -5, 10-10= 0, 15-10= 5
Find (x-x̄)²: -5²=
25 , 0²=
0 , 5²=
25
=25
Use the information below to find the value of the Pooled variance.
Brand n x̄ s² A 9 5 9 B 9 10 10 C 9 15 14
A. Pooled Variance = 8
B. Pooled Variance = 4.
C. Pooled Variance = 11.
D. Pooled Variance = 10.
C.
Pooled Variance= ((n1-1)(s²1)+(n2-1)(s²2)) / (n1 + n2 - 2) = ((9-1)(9)+(9-1)(10)+(9-1)(14)) / (27-3) =11
In this case, since there is 3 brands, instead of stopping at n2, you do the same formula with n3.
Use the information below to find the value of the Theoretical Variance.
Brand n x̄ s² A 9 5 19 B 9 10 13 C 9 15 22
s²_pooled= 18
A. Theoretical Variance= 18
B. Theoretical Variance= 2
C. Theoretical Variance= 6
D. Theoretical Variance= 10
B.
Theoretical variance= s²_pooled / n = 18 / 9 =2
Use the information below to find the value of the ANOVA fraction.
Brand n x̄ s² A 9 5 19 B 9 10 13 C 9 15 22
s²actual= 25 s²theoretical= 6
A. The ANOVA fraction = 0.24
B. The ANOVA fraction = 7.2
C. The ANOVA fraction = 4.2
D. The ANOVA fraction = 12.5
C.
ANOVA= Actual / Theoretical = 25/6 =4.2
Use the information below to find the value of the Actual Variance.
Car n x̄ s² Chevy 16 100 19 Ford 16 110 21 Chrysler 16 120 23
A. Actual Variance = 21
B. Actual Variance = 100
C. Actual Variance = 66
D. Actual Variance = 200
B.
Find average: (100+110+120)/3= 110
Find (x-x̄): 100-110= -10, 110-110= 0, 120-110= 10
Find (x-x̄)²: -10²= 100, 0²= 0, 10²= 100
(100+0+100)/ n-1 = 200 / 3-1
=100
Use the information below to find the value of the Pooled variance.
Car n x̄ s² Chevy 16 100 19 Ford 16 110 21 Chrysler 16 120 26
A. Pooled variance = 22
B. Pooled variance = 21
C. Pooled variance = 4
D. Pooled variance = 16
A.
Pooled Variance= ((n1-1)(s²1)+(n2-1)(s²2)) / (n1 + n2 - 2) = ((16-1)(19)+(16-1)(21)+(16-1)(26)) / (48-3) = 22
In this case, since there is 3 brands, instead of stopping at n2, you do the same formula with n3.
Use the information below to find the value of the Theoretical Variance.
Car n x̄ s² Chevy 16 100 119 Ford 16 110 121 Chrysler 16 120 126
s²pooled= 122
A. Theoretical Variance= 40.7
B. Theoretical Variance= 70.4
C. Theoretical Variance= 30.5
D. Theoretical Variance= 7.6
D.
Theoretical variance= s²_pooled / n = 122/16 =7.6
Use the information below to find the value of the ANOVA fraction (called the F test statistic).
Car n x̄ s² Chevy 16 100 119 Ford 16 110 121 Chrysler 16 120 126
s²actual= 100 s²theoretical= 40.6
A. The ANOVA fraction = 0.41
B. The ANOVA fraction = 15.69
C. The ANOVA fraction = 9.85
D. The ANOVA fraction = 2.46
D.
ANOVA= Actual / Theoretical = 100/40.6 = 2.46
Use the information below to find the value of the Actual Variance for the number of calories in three types of hot dogs.
Type n x̄ s² Beef 10 168.6 338.2 Meat 10 165.1 445.0 Poultry 10 107.1 203.2
A. Actual Variance = 1,193
B. Actual Variance = 396
C. Actual Variance = 795
D. Actual Variance = 1,541
A.
Find average: (168.6+165.1+107.1)/3= 146.9
Find (x-x̄): 168.6-146.9=
21.7 , 165.1-146.9=
18.2 , 107.1-146.9=
-39.8
Find (x-x̄)²: 21.7²=
470.89 , 18.2²=
331.24 , -39.8²=
1,584.04
(470.89+331.24+(-1,584.04)/ n-1 = -781.91 / 3-1
= 1,193
Use the information below to find the value of the Pooled variance for the number of calories in three types of hot dogs.
Type n x̄ s² Beef 10 168.6 338.2 Meat 10 165.1 445.0 Poultry 10 107.1 203.2
A. Pooled variance = 493.2
B. Pooled variance = 246.6
C. Pooled variance = 569.5
D. Pooled variance = 328.8
D.
Pooled Variance= ((n1-1)(s²1)+(n2-1)(s²2)) / (n1 + n2 - 2) = ((10-1)(338.2)+(10-1)(445)+(10-1)(203.2)) / (30-3) = 328.8
In this case, since there is 3 brands, instead of stopping at n2, you do the same formula with n3.
Use the information below to find the value of the Theoretical Variance for the number of calories in three types of hot dogs.
Type n x̄ s² Beef 10 168.6 338.2 Meat 10 165.1 445.0 Poultry 10 107.1 203.2
s²pooled= 328.8
A. Theoretical Variance = 109.6
B. Theoretical Variance = 32.9
C. Theoretical Variance = 104.0
D. Theoretical Variance = 29.9
B.
Theoretical variance= s²_pooled / n = 328.8/16 = 32.9
Use the information below to find the value of the ANOVA fraction (called the F test statistic) for the number of calories in three types of hot dogs.
Type n x̄ s² Beef 10 168.6 338.2 Meat 10 165.1 445.0 Poultry 10 107.1 203.2
s²actual= 1,193
s²theoretical= 32.9
A. The ANOVA fraction = 0.03
B. The ANOVA fraction = 36.26
C. The ANOVA fraction = 20.9
D. The ANOVA fraction = 108.8
B.
ANOVA= Actual / Theoretical = 1,193/32.9 = 36.26
Use the information below to find the value of the Actual Variance for the amount of sodium in three types of hot dogs.
Type n x̄ s² Beef 10 433.4 7,339 Meat 10 451.1 4,169 Poultry 10 427.0 5,284
A. Actual Variance = 45.0
B. Actual Variance = 155.8
C. Actual Variance = 316.7
D. Actual Variance = 103.9
B.
Find average: (433.4+451.1+427.0)/3= 437.2
Find (x-x̄): 433.4-437.2=
-3.8 , 451.1-437.2=
13.9 , 427-437.1=
-10.1
Find (x-x̄)²: -3.8²=
14.4 , 13.9²=
193.21 , -10.1²=
102.0
(14.4+193.21+102)/ n-1 = 309.6 / 3-1
= 155.8
Use the information below to find the value of the Pooled variance for the amount of sodium in three types of hot dogs.
Type n x̄ s² Beef 10 433.4 7,339 Meat 10 451.1 4,169 Poultry 10 427.0 5,284
A. Pooled variance = 4,198
B. Pooled variance = 5,284
C. Pooled variance = 8,396
D. Pooled variance = 5,597
D.
Pooled Variance= ((n1-1)(s²1)+(n2-1)(s²2)) / (n1 + n2 - 2) = ((10-1)(7,339)+(10-1)(4,169)+(10-1)(5,284)) / (30-3) = 5,597
In this case, since there is 3 brands, instead of stopping at n2, you do the same formula with n3.
Use the information below to find the value of the Theoretical Variance for the amount of sodium in three types of hot dogs.
Type n x̄ s² Beef 10 433.4 7,339 Meat 10 451.1 4,169 Poultry 10 427.0 5,284
s²pooled= 5,597
A. Theoretical Variance = 1,770
B. Theoretical Variance = 621.9
C. Theoretical Variance = 559.7
D. Theoretical Variance = 1,866
C.
Theoretical variance= s²_pooled / n = 5,597/10 = 559.7
Use the information below to find the value of the ANOVA fraction (called the F test statistic) for the amount of sodium in three types of hot dogs.
Type n x̄ s² Beef 10 433.4 7,339 Meat 10 451.1 4,169 Poultry 10 427.0 5,294
s²actual= 155.8
s²theoretical= 559.7
A. The ANOVA fraction = 3.59
B. The ANOVA fraction = 0.28
C. The ANOVA fraction = 0.88
D. Theoretical Variance = 2.78
B.
ANOVA= Actual / Theoretical = 155.8/559.7 = 0.28