Deck 16: Appendix 16 A: Analysis of Variance

Question 1

Which procedure(s) can be used to test the difference between two means when the population variance is unknown?

A) z statistic
B) t statistic
C) analysis of variance (ANOVA)
D) a and c above
E) b and c above

Answer 1

b and c above

Question 2

To compare three means in an analysis of variance (ANOVA), what form(s) of variance must be estimated?

A) the average of within and between group variance
B) within-group variance
C) between group variance
D) all of the above
E) b and c above

Answer 2

b and c above

Question 3

Which of the following is NOT a necessary assumption for the application of the analysis of variance (ANOVA)?

A) Samples are independent.
B) The variable is normally distributed.
C) The variance is the same for each treatment.
D) More than two means are being compared.
E) All of the above are necessary assumptions for the application of ANOVA.

Answer 3

More than two means are being compared.

Question 4

Which of the following is NOT a basic assumption of analysis of variance with a completely randomized design?

A) The treatment group means are equal.
B) The variance is the same for each treatment group.
C) The variable is normally distributed.
D) Samples are independent.
E) All of the above are basic assumptions of the analysis of variance.

Question 5

When using the analysis of variance technique, the hypothesis of equality of population means will be rejected if

A) the variance within groups is significantly greater than the variance between groups.
B) the variance between groups is significantly greater than the variance within groups.
C) the total variance is significantly greater than the variance within groups.
D) the total variance is significantly greater than the variance between groups.
E) the total variance is significantly greater than either the variance between groups or the variance within groups.

Question 6

In a randomized block experimental design, which of the following statements is INCORRECT?

A) All the assumptions necessary for a completely randomized design are necessary for the randomized block design as well.
B) The number of categories for each of the extraneous or blocked variables must be equal to the number of treatments.
C) Treatment effects are assumed to be additive.
D) The model underlying the randomized block design holds that the 8th observation on the j^th treatment results from the overall mean plus the treatment effect j plus the effect of the i^th block, plus random error.
E) All of the above are correct statements.

Question 7

Which of the following is NOT one of the reasons one would use a factorial experimental design?

A) Factorial experimental designs enable the researcher to control and eliminate variation from other variables affecting the dependent variable.
B) A factorial design enables the researcher to study interaction effects.
C) Factorial designs save both time and resources.
D) Factorial designs have broader applications than simple one factor designs.
E) All of the above are reasons for using a factorial experimental design.

Question 8

The value of the F statistic in analysis of variance is estimated using which of the following formulas (where MS is mean squares, SS is sum of squares, W is within, B is between, and T is total)?

A) MS_W/MS_B.
B) SS_W/SS_B.
C) MS_W/MS_T.
D) MS_B/MS_W.
E) SS_B/SS_W.

Question 9

Which of the following statements pertaining to randomized block designs is false?

A) The design is appropriate when one source of extraneous variation is distorting the results of the experiment.
B) The test units within each block are likely to be less alike than units selected completely at random.
C) Similar test units are grouped together.
D) Treatments are randomly assigned to test units within each block.
E) The error mean square in a randomized block design should be smaller than if a completely randomized design was used.

Question 10

When there is one source of extraneous variation distorting the results of an experiment, the preferred experimental design is

A) a contingency table.
B) a Latin Square design.
C) a factorial design.
D) a randomized block design.
E) a completely randomized design.

Question 11

Use the following situation to answer the next seven questions.
A researcher is interested in studying the effect of geographic location of grocery stores on the prices they charge for various food items. A typical "market basket" is selected and the researcher obtains data on the total basket price from 15 randomly selected stores as shown below. Note that 5 of the stores were inner city stores, 5 suburban stores and 5 campus stores.


-The between-group sum-of-squares in the above problem is calculated as

A)
B)
C)
D)
E) none of the above.

Question 12

Use the following situation to answer the next seven questions.
A researcher is interested in studying the effect of geographic location of grocery stores on the prices they charge for various food items. A typical "market basket" is selected and the researcher obtains data on the total basket price from 15 randomly selected stores as shown below. Note that 5 of the stores were inner city stores, 5 suburban stores and 5 campus stores.


-The within-group sum-of-squares in the above problem is calculated as

A)
B)
C)
D)
E) none of the above.

Question 13

Use the following situation to answer the next seven questions.
A researcher is interested in studying the effect of geographic location of grocery stores on the prices they charge for various food items. A typical "market basket" is selected and the researcher obtains data on the total basket price from 15 randomly selected stores as shown below. Note that 5 of the stores were inner city stores, 5 suburban stores and 5 campus stores.


-The total sum-of-squares in the above problem is calculated as

A)
B)
C)
D)
E) none of the above

Question 14

Use the following situation to answer the next seven questions.
A researcher is interested in studying the effect of geographic location of grocery stores on the prices they charge for various food items. A typical "market basket" is selected and the researcher obtains data on the total basket price from 15 randomly selected stores as shown below. Note that 5 of the stores were inner city stores, 5 suburban stores and 5 campus stores.


-The degrees of freedom associated with the between-group sum-of-squares in the above problem is

A) 2.
B) 3.
C) 12.
D) 14.
E) 15.

Question 15

Use the following situation to answer the next seven questions.
A researcher is interested in studying the effect of geographic location of grocery stores on the prices they charge for various food items. A typical "market basket" is selected and the researcher obtains data on the total basket price from 15 randomly selected stores as shown below. Note that 5 of the stores were inner city stores, 5 suburban stores and 5 campus stores.


-The degrees of freedom associated with the within-group sum-of-squares in the above problem is

A) 2.
B) 3.
C) 12.
D) 14.
E) 15.

Question 16

Use the following situation to answer the next seven questions.
A researcher is interested in studying the effect of geographic location of grocery stores on the prices they charge for various food items. A typical "market basket" is selected and the researcher obtains data on the total basket price from 15 randomly selected stores as shown below. Note that 5 of the stores were inner city stores, 5 suburban stores and 5 campus stores.


-The degrees of freedom associated with the total sum-of-squares in the above problem is

A) 2.
B) 3.
C) 12.
D) 14.
E) 15.

Question 17

A grocery store manager decided to investigate whether slower moving items would sell quicker if these items were displayed at the end of the grocery store aisles or with a special florescent shelf tag displaying the price. The manager is interested in these nonprice reduction promotions because the store has only a small markup on these items. The manager decides to use end of aisle displays, shelf markers, and no special markers for four weeks each measuring unit sales at the end of each week. The following sales patterns were observed:

(Use the above information to answer the following three questions.)

-How many degrees of freedom does the denominator of the F ratio in the ANOVA table have?

A) 2
B) 11
C) 9
D) 6
E) none of the above

Question 18

A grocery store manager decided to investigate whether slower moving items would sell quicker if these items were displayed at the end of the grocery store aisles or with a special florescent shelf tag displaying the price. The manager is interested in these nonprice reduction promotions because the store has only a small markup on these items. The manager decides to use end of aisle displays, shelf markers, and no special markers for four weeks each measuring unit sales at the end of each week. The following sales patterns were observed:

(Use the above information to answer the following three questions.)

-What is the within groups (error) sum of squares?

A) 86.0
B) 241.0
C) 98.0
D) 327.0
E) 26.8

Question 19

A grocery store manager decided to investigate whether slower moving items would sell quicker if these items were displayed at the end of the grocery store aisles or with a special florescent shelf tag displaying the price. The manager is interested in these nonprice reduction promotions because the store has only a small markup on these items. The manager decides to use end of aisle displays, shelf markers, and no special markers for four weeks each measuring unit sales at the end of each week. The following sales patterns were observed:

(Use the above information to answer the following three questions.)

-The calculated F ratio for this example demonstrates that at =0.05

A) there is a significant difference in sales between the displays, and the store manager should use bright shelf markers.
B) there is a significant difference in sales using the displays, but the manager cannot use this experiment to infer bright shelf markers are more effective than end of aisle displays.
C) no significant difference is found in the sales of this item under the three conditions.
D) no significant difference is found in the sales of this item and the store manager can conclude that shelf markers do not lead to increased sales of this item.
E) not enough information is provided to calculate the F ratio.

Question 20

Which of the following is NOT an assumption of the randomized block design?

A) X is normally distributed in each of the populations.
B) The variance of the variable in each population is the same.
C) The block and treatment effects are additive.
D) A random sample of size one is drawn from each of the kr (k treatments times r blocks) populations.
E) The means of the populations are not equal.

Question 21

When there are two extraneous factors that can cause serious distortion of the results, the preferred experimental design is

A) a factorial design.
B) a randomized block design.
C) a Latin Square design.
D) a covariance analysis.
E) a contingency table.

Question 22

Which of the following statements pertaining to Latin Square design is FALSE?

A) When the Latin Square design is used, the number of categories for each of the extraneous variables the researcher wishes to control must be greater than the number of treatments.
B) The Latin Square design is preferred to a randomized block design when there are two specific extraneous sources of error to be controlled.
C) Every treatment is used once with each category of each blocking variable in a Latin Square design.
D) The Latin Square design requires that the number of categories for each of the extraneous variables we wish to control be equal to the number of treatments.
E) All of the above are true.

Question 23

In the following model for the two-way factorial model, which term represents the interaction between the two factors?
X_ijk = µ + _i + ß_j + (11eec989_9808_301a_b236_a76dcd5d2dec_TB10464_11_iß)_ij + _ijk

A) µ
B)11eec989_9808_301a_b236_a76dcd5d2dec_TB10464_11_i
C) ß_j
D) 11eec989_ac87_886b_b236_f374e3ccc19b_TB10464_11_ijk
E) none of the above

Question 24

The effects of two or more treatment variables can be considered simultaneously in

A) a Latin Square design.
B) a randomized block design.
C) a covariance analysis.
D) a factorial design.
E) they can never be considered simultaneously but rather the analyst must conduct separate experiments to investigate their separate impacts.

Question 25

Which of the following statements regarding factorial designs is FALSE? A factorial design

A) may be needed to study the interaction of factors.
B) may save time and effort since all the observations are employed to study the effects of each of the factors.
C) may produce conclusions with broader applications since each factor can be studied with varying combinations of the other factors.
D) may be used in conjunction with a randomized block design.
E) they are all true.

Question 26

(Use the following information to answer the next six questions.)
A manufacturer is interested in selecting one of three companies to deliver (by truck) its product to its distributors and wholesalers in a certain area. Each of the companies has different operating procedures and uses different routes. Assuming that certain minimum standards for delivery time are achieved, the manufacturer wants to select the company with the lowest unit shipping cost.
In addition, the manufacturer believes that the type of packaging used for the product may have an impact on shipping cost and is considering two types of packaging. It is unknown whether or not any of the three companies under consideration is better equipped to handle either type of packaging.
After using each of the companies for five deliveries of the product with each of the types of packaging (thus, each company made a total of 10 deliveries, with all deliveries under similar circumstances), the shipping costs per unit were calculated and are shown below:


-Which of the following is the sum of squares for package design in the above problem?

A) 0.398
B) 3.156
C) 2.786
D) 0.133
E) none of the above

Question 27

(Use the following information to answer the next six questions.)
A manufacturer is interested in selecting one of three companies to deliver (by truck) its product to its distributors and wholesalers in a certain area. Each of the companies has different operating procedures and uses different routes. Assuming that certain minimum standards for delivery time are achieved, the manufacturer wants to select the company with the lowest unit shipping cost.
In addition, the manufacturer believes that the type of packaging used for the product may have an impact on shipping cost and is considering two types of packaging. It is unknown whether or not any of the three companies under consideration is better equipped to handle either type of packaging.
After using each of the companies for five deliveries of the product with each of the types of packaging (thus, each company made a total of 10 deliveries, with all deliveries under similar circumstances), the shipping costs per unit were calculated and are shown below:


-The sum of squares for the interaction term in the above problem can be calculated as

A)
B) SS_PC - SS_P - SS_C.
C) SS_T - SS_TR.
D) SS_TR - SS_P - SS_C.
E) none of the above.

Question 28

(Use the following information to answer the next six questions.)
A manufacturer is interested in selecting one of three companies to deliver (by truck) its product to its distributors and wholesalers in a certain area. Each of the companies has different operating procedures and uses different routes. Assuming that certain minimum standards for delivery time are achieved, the manufacturer wants to select the company with the lowest unit shipping cost.
In addition, the manufacturer believes that the type of packaging used for the product may have an impact on shipping cost and is considering two types of packaging. It is unknown whether or not any of the three companies under consideration is better equipped to handle either type of packaging.
After using each of the companies for five deliveries of the product with each of the types of packaging (thus, each company made a total of 10 deliveries, with all deliveries under similar circumstances), the shipping costs per unit were calculated and are shown below:


-The sum of squares for a company is 2.786. What is the mean square for a company?

A) 2.786
B) 0.929
C) 1.393
D) 7.762
E) none of the above

Question 29

(Use the following information to answer the next six questions.)
A manufacturer is interested in selecting one of three companies to deliver (by truck) its product to its distributors and wholesalers in a certain area. Each of the companies has different operating procedures and uses different routes. Assuming that certain minimum standards for delivery time are achieved, the manufacturer wants to select the company with the lowest unit shipping cost.
In addition, the manufacturer believes that the type of packaging used for the product may have an impact on shipping cost and is considering two types of packaging. It is unknown whether or not any of the three companies under consideration is better equipped to handle either type of packaging.
After using each of the companies for five deliveries of the product with each of the types of packaging (thus, each company made a total of 10 deliveries, with all deliveries under similar circumstances), the shipping costs per unit were calculated and are shown below:


-If the mean square for error is 0.168, compute the F ratio necessary to determine whether a difference exists between the three companies with regard to unit shipping costs. (Note: take advantage of any previous calculations useful for this question.) The F ratio is

A) 8.292.
B) 2.369.
C) 0.000.
D) 199.000.
E) none of the above.

Question 30

(Use the following information to answer the next six questions.)
A manufacturer is interested in selecting one of three companies to deliver (by truck) its product to its distributors and wholesalers in a certain area. Each of the companies has different operating procedures and uses different routes. Assuming that certain minimum standards for delivery time are achieved, the manufacturer wants to select the company with the lowest unit shipping cost.
In addition, the manufacturer believes that the type of packaging used for the product may have an impact on shipping cost and is considering two types of packaging. It is unknown whether or not any of the three companies under consideration is better equipped to handle either type of packaging.
After using each of the companies for five deliveries of the product with each of the types of packaging (thus, each company made a total of 10 deliveries, with all deliveries under similar circumstances), the shipping costs per unit were calculated and are shown below:


-The degrees of freedom associated with the error sum of squares in the above problem is(are)

A) 1.
B) 2.
C) 29.
D) 24.
E) none of the above.

Question 31

In an experiment testing the effectiveness of five different advertisements for a new product in five separate markets, sales of the new product are recorded at the end of each week for eight weeks. Analysis of variance is used to investigate whether the advertisements are equally successful.

-The total number of degrees of freedom for the design is

A) 35.
B) 4.
C) 7.
D) 28.
E) 39.

Question 32

In an experiment testing the effectiveness of five different advertisements for a new product in five separate markets, sales of the new product are recorded at the end of each week for eight weeks. Analysis of variance is used to investigate whether the advertisements are equally successful.

-If the sum of squares for the factor "Advertisements" is 168, the mean square for this variable is

A) 42.
B) 21.
C) 24.
D) 33.6.
E) not able to be calculated.

Question 33

In an experiment testing the effectiveness of five different advertisements for a new product in five separate markets, sales of the new product are recorded at the end of each week for eight weeks. Analysis of variance is used to investigate whether the advertisements are equally successful.

-If the sum of squares for the error term in this example is 1,050, what is the calculated F ratio?

A) 30
B) 1.40
C) 0.70
D) 1.12
E) The F ratio cannot be calculated with the information provided.