Multiple Choice Exercise

*** Choose one answer and click [Submit] button

9.1 Who first announced the ANOVA method?





        

9.2 What are the abbreviation of the analysis of variance?





        

9.3 Which areas are not the area of application for the analysis of variance?





        

9.4 Which sampling distribution is used for the analysis of variance?





        

9.5 Which is the correct process for the one-way ANOVA?

a. Calculate Total SS, Treatment SS, Error SS
b. Set the hypothesis
c. Test the hypothesis
d. Calculate the variance ration in the ANOVA table
e. Find the value in the F distribution table





        

9.6 Which is the correct relationship between the total sum of squares (SST), between sum of squares (SSB), error sum of squares (SSE)?





        

9.7 If \(F_{4,30: 0.05} = 2.87\) and the observed \(F\) ratio is 6.90 in the ANOVA table, what is your conclusion with the 5％ significance level?





        

9.8 Which is not appeared in the analysis of variance table?





        

9.9 What is the name of variable which effects response variable in the experimental design?





        

9.10 In order to compare the fuel mileage of three types of cars, three drivers would like to drive cars, but fuel mileage may be affected by the driver. What is the name of variable like drivers?





        

9.11 When we compare the fuel mileage of three types of cars, which experimental design is used to reduce the effect of drivers?





        

9.12 What is called the effect of a factor A that varies depending on the level of the factor B?





        

Practice Exercise

*** Answer the followings

9.1 Complete the following ANOVA table.

Factor SS df MS F ratio
Treatment 154.9199 4
Error
Total 200.4773 39

9.2 Answer the following questions based on this ANOVA table.

Factor SS df MS F ratio
Treatment 5.05835 2 2.52917 1.0438
Error 65.42090 27 2.4230

1) How many levels of treatment are compared?
2) How many total number of observations are there?
3) Can you conclude that the levels of treatment are significantly different with the 5% significance level? Why?

9.3 In order to test customers' responses to new products, four different exhibition methods (A, B, C and D) were used by a company. Each exhibition method was used in nine stores by selecting 36 stores that met the company's criteria. The total sales in USD for the weekend are shown in the following table.

Method A Method B Method C Method D
5 2 2 6
6 2 2 6
7 2 3 7
7 3 3 8
8 3 2 8
6 2 2 8
7 3 2 6
7 3 3 6
6 2 3 6

1) Draw a scatter plot of sales (y axis) and exhibition method (x axis). Mark the average sales of each exhibition method and connect them with a line.
2) Test that the sales by each exhibition method are different in the amount of sales with the 5% significance level. Can you conclude that one of the exhibition methods shows significant effect on sales?

9.4 The following table shows mileages in km per one liter of gasoline obtained from experiments to compare three brands of gasoline. In this experiment, seven cars of the same type were used in a similar situation to reduce the variation of the car.

Gasoline A Gasoline B Gasoline C
14 20 20
19 21 26
19 18 23
16 20 24
15 19 23
17 19 25
20 18 23

1) Calculate the average mileages of each gasoline brand. Draw a scatter plot of gas milage (y axis) and gasoline brand (x axis) to compare.
2) From this data, test whether there are differences between gasoline brands for gas milage with the 5% significance level.

9.5 The result of a survey on job satisfaction of three companies (A, B, and C) is as follows: Test whether the averages of job satisfaction of the three companies are different with the 5% significance level.

Company A Company B Company C
69 56 71
67 63 72
65 55 70
59 59 68
68 52 74
61 57
66

9.6 Psychologists were asked to investigate the job satisfaction of salespeople in three companies: A, B and C. Ten salespeople were randomly selected from each company and a test to measure the job satisfaction was conducted. Test scores are as follows: From this data, can we claim that the average scores of the job satisfaction of three companies are different with the significance level of 0.05?

Company A Company B Company C
67 66 87
65 68 80
59 55 67
59 59 89
58 61 80
61 66 84
66 62 78
53 65 65
51 64 72
64 74 85

9.7 An advertising agency experimented to find out the effects of various forms (A, B, C, D and E) of TV advertising. Fifty television viewers were shown five forms of TV commercials for a cold medicine in random order one by one. The effect of advertising after viewing was measured and recorded as follows: Test an appropriate hypothesis with the 5% significance level.

Method A Method B Method C Method D Method E
20 28 33 33 49
23 27 34 29 41
21 22 25 31 41
23 28 26 29 39
26 23 27 27 41
24 29 33 25 48
26 27 25 26 43
23 25 32 26 43
20 28 25 33 46
24 21 34 32 35

9.8 The following is the result of an agronomist's survey of the yield of four varieties of wheat by using the randomized block design of three cultivated areas (block). Test whether the mean yields of the four wheats are the same or not with the 5% significance level.

Wheat Type Area 1 Area 2 Area 3 Average
Wheat A 60 61 56 59
Wheat B 59 52 51 54
Wheat C 55 55 52 54
Wheat D 58 58 55 57

9.9 Answer the following questions based on the following ANOVA table.

Factor SS df MS F ratio p-value
A 12.3152 2 6.1575 29.4021 < 0.005
B 19.7844 3 6.5948 31.4898 < 0.005
AB 8.9416 6 1.4902 7.1159 < 0.005
Error 10.0525 48 0.2094
Total 51.0938 59

1) What method of analysis was used?
2) What conclusions can be obtained from the above analysis table? The significance level is 0.05.

9.10 Research was conducted to compare the job satisfaction of workers in the assembly process with different working conditions. Another concern is the relationship between the job satisfaction and years of service. Observers would like to investigate the interaction effect between the years of service and working conditions. The following table shows the level of the job satisfaction obtained from the survey. Analyze the data using an appropriate methodology.

Years of service Good Fair Bad
< 5 12
15
15
14
12		 10
10
9
10
9		 8
7
7
8
6
5 - 10 12
14
12
10
11		 10
10
14
14
10		 10
11
12
10
14
11 or more 9
10
9
9
10		 10
11
10
10
12		 12
14
15
15
15

9.11 The following table shows the degree of stress in the work and the level of anxiety among 27 workers classified as years of service. Analyze data using the analysis of variance with the 5% significance level.

Factor A
Years of Service		 Job Pressure
Good		 Job Pressure
Fair		 Job Pressure
Bad
< 5 25
28
22		 18
23
19		 17
24
19
5 - 10 28
32
30		 16
24
20		 18
22
20
11 or more 25
35
30		 14
16
15		 10
8
12

9.12 A fertilizer manufacturer hired a research team to study the yields of three grain seeds (A, B, C) and three types of fertilizer (1, 2, 3). Three grain seeds in combination of three types of fertilizer were used and the experiment were repeated three times at each combination of treatments. Each combination of treatments was randomly assigned to 27 different regions. Analyze data using the analysis of variance with the 5% significance level.

Seed Type Fertilizer 1 Fertilizer 2 Fertilizer 3
A 5
8
7 		8
8
10 		10
9
10
B 6
8
6		 10
12
11		 15
14
14
C 7
8
10		 12
12
14		 16
10
18

9.13 The result of a fertilizer manufacturer's experiment with the production of soybeans on two seeds using three types of fertilizer (A, B, and C) is as follows: Each fertilizer and seed were tested four times. Analyze data using the analysis of variance with the 5% significance level.

Fertilizer A Fertilizer B Fertilizer C
Seed 1 5
8
7
6		 8
8
10
10		 10
12
10
10
Seed 2 8
6
8
10		 12
11
12
14		 14
16
16
18