Deck 14: Analysis of Variance

Question 1

How many degrees of freedom are there for SSE.

A) 3
B) 18
C) 2
D) 19

Answer 1

19

Question 2

Samples were drawn from three populations. The sample sizes were n₁=8, n₂=8, and n₃=7 . The sample means were , and =2.57 . The sample standard deviations were s₁=0.27, s₂=0.45, and s₃=0.25 . The grand mean is =2.055217.

i). Compute the sums of squares SSTr and SSE.
ii). How many degrees of freedom are there for SSTr and SSE?
iii). Compute the sums of squares MSTr and MSE.
iv). Compute the value of the test statistic F.
v). Can you conclude that two or more of the population means are different? Use the level of
significance.

Answer 2

i). SSTr = 2.8970; SSE = 2.3028
ii). degrees of freedom for SSTr = 2; degrees of freedom for SSE = 20
iii). MSTr = 1.4485; MSE = 0.1151
iv). 12.580
v). Yes

Question 3

In a one-way ANOVA, the following data were collected: How many samples are there?

A) 17
B) 5
C) 4
D) 22

Answer 3

5

Question 4

Compute the sum of squares SSTr.

A) 2.6317
B) 0.2604
C) 0.1302
D) 0.8905

Question 5

Compute the mean squares MSE.

A) 1.5610
B) 2.3847
C) 0.1325
D) 0.7805

Question 6

The following table shows the weekly total sales (in dollars) at a small roadside vegetable stand for the months June through September. Can you conclude that the weekly sales varies with the month? Use the level of significance.

A) No
B) Yes

Question 7

Compute the sum of squares SSE.

A) 0.7919
B) 0.3959
C) 3.7611
D) 2.1055

Question 8

In a one-way ANOVA, the following data were collected: SSTr = 0.42, SSE = 2.15, N = 30, I = 4.
i). How many samples are there?
ii). How many degrees of freedom are there for SSTr and SSE?
iii). Compute the mean squares MSTr and MSE.
iv). Compute the value of the test statistic F.

Question 9

One of the factors that determines the degree of risk a pesticide poses to human health is the rate at
which it is absorbed into the skin after contact. An important question is whether the amount in the
skin continues to increase with the length of the contact, or whether it increases for only a short time
before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20
samples of rat skin. Four skins were analyzed at each of the time intervals 1, 2, 4, 10, and 24 hours. The
amounts of the chemical (in micrograms) that were in the skin are given in the following table:

Question 10

How many degrees of freedom are there for SSTr.

A) 2
B) 3
C) 24
D) 23

Question 11

Can you conclude that two or more of the population means are different? Use the α = 0.05 level of significance.

A) No
B) Yes

Question 12

In a one-way ANOVA, the following data were collected: SSTr = 0.49, SSE = 2.2, N = 35, I = 4. Compute the mean squares MSE.

A) 0.0158
B) 0.0710
C) 0.1633
D) 2.3015

Question 13

The following table shows the weekly total sales (in dollars) at a small roadside vegetable stand for
the months June through September. i). Construct an ANOVA table.
ii). Can you conclude that the weekly sales varies with the month? Use the level of significance.

Question 14

Compute the mean squares MSTr.

A) 3.0039
B) 1.2667
C) 0.2114
D) 0.4228

Question 15

The following table shows the weekly total sales (in dollars) at a small roadside vegetable stand for the months June through September. Perform a Tukey-Kramer test to determine which pairs of means, if any, differ. Use the level of Significance.

A)
B)
C)
D) There is not enough evidence to conclude that any of the means differ.

Question 16

In a one-way ANOVA, the following data were collected: SSTr = 0.3, SSE = 1.55, N = 35, I = 6. Compute the mean squares MSTr.

A) 0.0534
B) 0.0103
C) 1.1226
D) 0.0600

Question 17

In a one-way ANOVA, the following data were collected: SSTr = 0.43, SSE = 1.87, N = 39, I = 5. How many degrees of freedom are there for SSTr?

A) 5
B) 39
C) 4
D) 34

Question 18

In a one-way ANOVA, the following data were collected: SSTr = 0.37, SSE = 2.31, N = 30, I = 3. Compute the value of the test statistic F.

A) 0.1850
B) 0.0137
C) 2.1623
D) 0.0856

Question 19

Compute the value of the test statistic F.

A) 0.782
B) 2.194
C) 0.101
D) 0.202

Question 20

In a one-way ANOVA, the following data were collected: SSTr = 0.43, SSE = 2.32, N = 33, I = 6. How many degrees of freedom are there for SSE?

A) 6
B) 27
C) 5
D) 33

Question 21

Artificial hip joints consist of a ball and socket. As the joint wears, the ball (head) becomes rough. Investigators performed wear tests on metal artificial; hip joints. Joints with several different Diameters were tested. The following table presents measurements of head roughness (in Nanometers). Perform the Tukey-Kramer test to determine which pairs of means, if any, differ. Use the level of Significance.

A) There is not enough evidence to conclude that any of the means differ.
B)
C)
D)

Question 22

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together End-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond Apart. For each combination of curing time and curing temperature, three tests are performed. The Results of the experiment are shown below. Can the main effect of curing temperature (low or high) on bonding strength be interpreted? If so, interpret the Main effect using the level of significance.

A) Yes. Do not reject H₀.
B) Yes. Reject H₀.
C) No.

Question 23

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
The mean fill volumes differ among the filling machines. What is the value of SSE?

A) 0.04625
B) 0.8025
C) 0.555
D) 0.2675

Question 24

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
The mean fill volumes differ among the filling machines. What is the value of the test statistic?

A) 0.4925
B) 6.459016
C) 0.025417
D) 0.007519

Question 25

Interpret the interaction plot by explaining whether there appear to be large interactions between factors.

A) Interactions are not large
B) Interactions are large

Question 26

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together
End-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond
Apart. For each combination of curing time and curing temperature, three tests are performed. The
Results of the experiment are shown below.

Can the main effect of curing time on bonding strength be interpreted? If so, interpret the main effect. using the level of significance.

A) Yes. Reject H₀
B) Yes. Do not reject H₀.
C) No.

Question 27

Artificial hip joints consist of a ball and socket. As the joint wears, the ball (head) becomes rough. Investigators performed wear tests on metal artificial; hip joints. Joints with several different
Diameters were tested. The following table presents measurements of head roughness (in
Nanometers). Can you conclude that the mean roughness varies with diameter? Use the level of significance.

A) Yes
B) No

Question 28

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
The mean fill volumes differ among the filling machines. What is the value of SSTr?

A) 0.049792
B) 0.5975
C) 0.152292
D) 0.456875

Question 29

Interpret the interaction plot by explaining whether there appear to be large interactions between factors.

A) Interactions are not large
B) Interactions are large

Question 30

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
The mean fill volumes differ among the filling machines. What is the P-value?

A) 0.326875
B) 0.022708
C) 4.798165
D) 0.020211

Question 31

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together
End-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond
Apart. For each combination of curing time and curing temperature, three tests are performed. The
Results of the experiment are shown below. Can you reject the hypothesis of no interactions?

A) No
B) Yes

Question 32

Artificial hip joints consist of a ball and socket. As the joint wears, the ball (head) becomes rough.
Investigators performed wear tests on metal, artificial hip joints. Joints with several different diameters were
tested. The following table presents measurements of head roughness (in nanometers). i). Construct an ANOVA table.
ii). Can you conclude that the mean roughness varies with diameter? Use the level of significance.

Question 33

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
The mean fill volumes differ among the filling machines. What is the value of MSE?

A) 0.3125
B) 0.365
C) 0.030417
D) 0.104167

Question 34

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
The mean fill volumes differ among the filling machines. Can you conclude that the mean fill volume differs among the filling machines? Use the level of
Significance.

A) No
B) Yes

Question 35

One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which it is absorbed into the skin after contact. An important question is whether the amount in the Skin continues to increase with the length of the contact, or whether it increases for only a short time Before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20 Samples of rat skin. Four skins were analyzed at each of the time intervals 1, 2, 4, 10, and 24 hours. The Amounts of the chemical (in micrograms) that were in the skin are given in the following table: Perform the Tukey-Kramer test to determine which pairs of means, if any, differ. Use the level of Significance.

A)
B) There is not enough evidence to conclude that any of the means differ.
C)
D)

Question 36

An experiment is conducted to study the effects of curing times and curing temperatures on the
bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together
end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond
apart. For each combination of curing time and curing temperature, three tests are performed. The
results of the experiment are shown below. i). Can you reject the hypothesis of no interactions?
ii). Can the main effect of curing temperature (low or high) on bonding strength be interpreted? If so, interpret
the main effect using the α = 0.05 level of significance.
iii). Can the main effect of curing time on bonding strength be interpreted? If so, interpret the main effect using
the level of significance.

Question 37

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water. The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
The mean fill volumes differ among the filling machines. What is the value of MSTr?

A) 0.111667
B) 0.305
C) 0.025417
D) 0.335

Question 38

In a water-bottling facility, several machines fill plastic bottles with 16 ounces of drinking water.
The following TI-84 Plus display presents the results of a one-way ANOVA to determine whether
the mean fill volumes differ among the filling machines. i). State the null hypothesis.
ii). How many filling machines were involved in the study?
iii). Assume the design was balanced. How many water bottles were measured for each filling machine?
iv). What are the values of SSTr, SSE, MSTr, and MSE?
v). What is the value of the test statistic?
vi). What is the P-value?
vii). Can you conclude that the mean fill volume differs among the filling machines? Use the level
of significance.

Question 39

One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which it is absorbed into the skin after contact. An important question is whether the amount in the
Skin continues to increase with the length of the contact, or whether it increases for only a short time
Before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20
Samples of rat skin. Four skins were analyzed at each of the time intervals 1, 2, 4, 10, and 24 hours. The
Amounts of the chemical (in micrograms) that were in the skin are given in the following table: Can you conclude the amount in the skin varies with time? Use the level of significance.

A) No
B) Yes

Question 40

Interpret the interaction plot by explaining whether there appear to be large interactions between factors.

A) Interactions are large
B) Interactions are not large

Question 41

An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following
MINITAB output presents the results. Can the mean effect of the soil mixture be interpreted? If so, interpret the main effect. Use the level Of significance.

A) Yes. Do not reject H₀.
B) Yes. Reject H₀.
C) No.

Question 42

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber
concrete beams for three levels of binder content and three levels of rubber content.
i). Can you reject the hypothesis of no interactions?
ii). Can the mean effect of the binder content be interpreted? If so, interpret the main effect. Use the level of significance.
iii). Can the mean effect of the rubber content be interpreted? If so, interpret the main effect. Use the level of significance.

Question 43

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content.
Can the mean effect of the rubber content be interpreted? If so, interpret the main effect. Use the a= level of significance.

A) Yes. Reject H₀
B) No.
C) Yes. Do not reject H₀

Question 44

An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil
mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following
MINITAB output presents the results. i). Can you reject the hypothesis of no interactions?
ii). Can the mean effect of the soil mixture be interpreted? If so, interpret the main effect. Use the α = 0.01
level of significance.
iii). Can the mean effect of the hybrid variety be interpreted? If so, interpret the main effect. Use the α = 0.01
level of significance.

Question 45

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content. Can you reject the hypothesis of no interactions?

A) Yes
B) No

Question 46

An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following
MINITAB output presents the results. Can you reject the hypothesis of no interactions?

A) No
B) Yes

Question 47

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content. Can the mean effect of the binder content be interpreted? If so, interpret the main effect. Use the = 0.01 Level of significance.

A) No.
B) Yes. Reject. H₀
C) Yes. Do not reject H₀

Question 48

An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following
MINITAB output presents the results. Can the mean effect of the hybrid variety be interpreted? If so, interpret the main effect. Use the α = 0.05 Level of significance.

A) Yes. Do not reject H₀.
B) Yes. Reject H₀.
C) No.