Appendix 16A
Analysis of Variance
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
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
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.
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.
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.
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 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.
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.
following formulas (where MS is mean squares, SS is sum of squares, W is within,
B is between, and T is total)?
a. MSW/MSB.
b. SSW/SSB.
c. MSW/MST.
d. MSB/MSW.
e. SSB/SSW.
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.
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.
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.
Campus Inner City Suburban
$56 $58 $55
60 61 60
50 48 44
65 52 46
_ 64 _ 46 _ 55
xC= 59 xI= 51 xS= 52
=
x = 54
a. a completely randomized design.
b. a randomized block design.
c. a Latin Square design.
d. a factorial design.
e. none of the above.
k nj _
a. Σ Σ (Xij – x..)2 = (56-54)2 + (60-54)2 + … + (55-54)2.
j=1 i=1
k _ _
b. Σ nj (x.j-x..)2 = 5(59-54)2 + … + 5(52-54)2.
j=1
k nj _
c. Σ Σ (Xij – x.j)2 = (56-59)2 + (60-59)2 + … + (55-54)2.
j=1 j=1
k _ _
d. Σ (x.j – x..)2 = (59-54)2 + … + (52-54)2.
j=1
e. none of the above.
k nj
a. Σ Σ (Xij – x..)2 = (56-54)2 + (60-54)2 + … + (55-54)2.
j=1 i=1
k
b. Σ nj (x.j-x..)2 = 5(59-54)2 + … + 5(52-54)2.
j=1
k nj
c. Σ Σ (Xij – x.j)2 = (56-59)2 + (60-59)2 + … + (55-54)2.
j=1 j=1
k
d. Σ (x.j – x..)2 = (59-54)2 + … + (52-54)2.
j=1
e. none of the above.
k nj
a. Σ Σ (Xij – x..)2 = (56-54)2 + (60-54)2 + … + (55-54)2.
j=1 i=1
k
b. Σ nj (x.j-x..)2 = 5(59-54)2 + … + 5(52-54)2.
j=1
k nj
c. Σ Σ (Xij – x.j)2 = (56-59)2 + (60-59)2 + … + (55-54)2.
j=1 j=1
k
d. Σ (x.j – x..)2 = (59-54)2 + … + (52-54)2.
j=1
e. none of the above
above problem is
a. 2.
b. 3.
c. 12.
d. 14.
e. 15.
above problem is
a. 2.
b. 3.
c. 12.
d. 14.
e. 15.
problem is
a. 2.
b. 3.
c. 12.
d. 14.
e. 15.
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:
End of Aisle Display
Bright Shelf Marker
No Special Promotion
6
20
18
14
18
10
19
23
11
17
11
7
(Use the above information to answer the following three questions.)
table have?
a. 2
b. 11
c. 9
d. 6
e. none of the above
a. 86.0
b. 241.0
c. 98.0
d. 327.0
e. 26.8
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.
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.
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.
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.
interaction between the two factors?
Xijk = µ + α i + ßj + (α ß)ij + ε ijk
a. µ
b. αi
c. ßj
d. εijk
e. none of the above
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.
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.
(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:
Company
Package C1 C2 C3 Total Mean
________________________________________________________________
$1.75 $1.25 $1.80
1.65 1.15 1.70
P1 1.90 1.35 1.95 24.30 1.62
2.00 1.15 1.75
1.70 1.15 2.05
________________________________________________________________
2.00 1.35 1.95
1.90 1.55 2.05
P2 2.15 1.35 2.30 27.80 1.85
2.25 1.35 2.00
1.95 1.45 2.20
________________________________________________________________
Total 19.25 13.10 19.75 52.10 1.74
Mean 1.93 1.31 1.98
Cell P1C1 P1C2 P1C3 P2C1 P2C2 P2C3
Total 9.00 6.05 9.25 10.25 7.05 10.50
Mean 1.80 1.21 1.85 2.05 1.41 2.10
a. a completely randomized design.
b. a randomized block design.
c. a Latin square design.
d. a factorial design.
e. none of the above.
problem?
a. 0.398
b. 3.156
c. 2.786
d. 0.133
e. none of the above
as
P C _ _
a. nΣ Σ (xij – x…)2= 5[(1.80-1.74)2+(1.21-1.74)2+…+(2.10-1.74)2].
i=1 j=1
b. SSPC – SSP – SSC.
c. SST – SSTR.
d. SSTR – SSP – SSC.
e. none of the above.
company?
a. 2.786
b. 0.929
c. 1.393
d. 7.762
e. none of the above
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.
problem is(are)
a. 1.
b. 2.
c. 29.
d. 24.
e. none of the above.
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.
a. 35.
b. 4.
c. 7.
d. 28.
e. 39.
this variable is
a. 42.
b. 21.
c. 24.
d. 33.6.
e. not able to be calculated.
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.