Question 1

In the following model for the two-way factorial model, which term represents the interaction between the two factors?
Xijk = µ + i + ßj + (iß)ij + ijk

Accepted Answer

A)  µ 
B) i 
C)  ßj 
D)  ijk 
E)  none of the above

Question 2

(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

Accepted Answer

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

Question 3

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

Accepted Answer

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.

Question 4

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

Accepted Answer

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 5

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

Accepted Answer

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 6

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)?

Accepted Answer

A)  MSW/MSB. 
B)  SSW/SSB. 
C)  MSW/MST. 
D)  MSB/MSW. 
E)  SSB/SSW.

Question 7

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

Accepted Answer

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 8

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

Accepted Answer

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 jth treatment results from the overall mean plus the treatment effect j plus the effect of the ith block, plus random error. 
E)  All of the above are correct statements.

Question 9

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

Accepted Answer

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 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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 12

(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?

Accepted Answer

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

Question 13

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

Accepted Answer

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

Exam 16: Appendix 16 A: Analysis of Variance

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 + 11eec989_ac87_886b_b236_f374e3ccc19b_TB10464_11_ijk

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

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

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

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) ?

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

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

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

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

Exam 16: Appendix 16 A: Analysis of Variance

In the following model for the two-way factorial model, which term represents the interaction between the two factors? Xijk = µ + i + ßj + (11eec989_9808_301a_b236_a76dcd5d2dec_TB10464_11iß) ij + 11eec989_ac87_886b_b236_f374e3ccc19b_TB10464_11ijk

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

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

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

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) ?

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

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

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

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

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 + 11eec989_ac87_886b_b236_f374e3ccc19b_TB10464_11_ijk