Deck 12: Analysis of Variance Tests

Question 1

Randomized block ANOVA examines interactions between different levels of the independent variables.

Answer 1

False

Question 2

Using the randomized block design allows the reduction of the amount of error variation.

Answer 2

True

Question 3

Comparing the variation between the groups to the variation within the groups is the basis of ANOVA.

Answer 3

True

Question 4

The one-way ANOVA is also referred to as the one-factor,completely randomized design,since the treatments are randomly assigned to all of the persons or other test units in the experiment.

Question 5

An assumption of the ANOVA model is that the population distributions are normal.

Question 6

In ANOVA,if the calculated F-statistic exceeds the critical F for a given test,the null hypothesis of equal population means is rejected.

Question 7

Analysis of variance (ANOVA) is a set of techniques that allow us to compare two or more sample means at the same time.

Question 8

In ANOVA,the independent variable must be quantitative.

Question 9

A study will be undertaken to examine the effect of two kinds of background music and of two assembly methods on the output of workers at a fitness shoe factory.Two workers will be randomly assigned to each of four groups,for a total of eight in the study.Each worker will be given a headphone set so that the music type can be controlled.The number of shoes completed by each worker will be recorded.Does the kind of music or the assembly method or a combination of music and method affect output? The ANOVA model most likely to fit this situation is the one-way analysis of variance.

Question 10

In the randomized block design,interaction is present when the effect of a treatment depends on the block to which it has been administered.

Question 11

In ANOVA,the variation between groups represents random error from the sampling process.

Question 12

Basic to ANOVA is the comparison of variation between samples versus the amount of variation within the samples.The test statistic is an F-ratio in which the numerator reflects variation within the samples and the denominator reflects the variation between them.

Question 13

When there are two treatment groups,one-way ANOVA is equivalent to the pooled-variances t-test.

Question 14

In two-way ANOVA,it is not appropriate to refer to the factor levels as treatments,since each combination of their levels constitutes a separate treatment.

Question 15

In the randomized block design ANOVA,test units are first arranged in similar groups after the treatments are assigned.

Question 16

The two-way ANOVA examines the main effects of the levels of both factors as well as interaction effects associated with the combinations of their levels.

Question 17

The ANOVA model requires that the sample size for each treatment be equal.

Question 18

Three racquetball players,a beginner,an experienced,a professional,have been randomly selected from the membership of a large city racquetball club.Using the same ball,each person hits three serves,one with each of five racquet models,with the five racquet models selected randomly.Each serve is clocked with a radar gun and the result recorded.Among ANOVA models,this setup is most like the two-way ANOVA.

Question 19

In two-way ANOVA,significance tests include those for the main effects of each factor,but not for interaction effects between the combinations of factor levels.

Question 20

In the randomized block design ,there is just one observation or measurement for each block-treatment combination.

Question 21

Two samples of ten each from the male and female workers of a large company have been taken.The data involved the wage rate of each worker.To test whether there is any difference in the average wage rate between male and female workers a pooled-variances t-test will be considered.Another test option to consider is ANOVA.The most likely ANOVA to fit this test situation is the:

A) one-way analysis of variance.
B) randomized block design.
C) two-way analysis of variance.
D) simple regression model.
E) chi-square test for independence.

Question 22

In employing the randomized block design,the primary interest lies in:

A) increasing the treatment sum of squares (SSTR).
B) reducing the block sum of squares (SSB).
C) improving the significance of any differences among treatment groups.
D) reducing the total sum of squares (SST).
E) increasing the total sum of squares (SST).

Question 23

One-way ANOVA is applied to three independent samples having means 10,13,and 18,respectively.If each observation in the third sample were increased by 30,the value of the F-statistic would:

A) increase.
B) decrease.
C) remain unchanged.
D) increase by 30.

Question 24

A balanced experiment requires that:

A) at least one sample equal size is 30.
B) the number of treatments equals the number of samples.
C) an equal number of persons or test units receives each treatment.
D) at least two treatment groups be used.
E) at least two samples are paired.

Question 25

Consider the following partial ANOVA table: $$\begin{array} { | l | l l l l | } \hline \text { Source of Variation } & \boldsymbol { S S } & \boldsymbol { d f } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Treatments } & 75 & * & 25 & 6.67 \\\text { Error } & 60 & * & 3.75 & \\\hline \text { Total } & 135 & 19 & & \\\hline\end{array}$$ The numerator and denominator degrees of freedom (identified by asterisks)are,respectively,

A) 4 and 15.
B) 3 and 16.
C) 15 and 4.
D) 16 and 3.

Question 26

The calculated value of F in a one-way analysis is 8.23.The numerator degrees of freedom and denominator degrees of freedom are 4 and 8,respectively.The most accurate statement to be made about the p-value is:

A) p-value > 0.05.
B) 0.05 > p-value > 0.025.
C) p-value > 0.01.
D) 0.01 > p-value.
E) 0.025 > p-value > 0.01.

Question 27

Given the significance level 0.01,the F-value for the degrees of freedom,df = (7,3)is:

A) 8.45.
B) 27.67.
C) 5.89.
D) 14.62.
E) 38.22.

Question 28

The numerator or MSTR degrees of freedom are 4 and the denominator or MSE degrees of freedom are 20. The total number of observations in the completely randomized design must equal:

A) 24.
B) 20.
C) 19.
D) 25.
E) 80.

Question 29

A randomized block design ANOVA has two treatments.The test to be performed in this procedure is equivalent to:

A) dependent samples z-test.
B) dependent samples t-test.
C) independent samples z-test.
D) independent samples t-test.
E) Spearman rank correlation test.

Question 30

The distribution of the test statistic for analysis of variance is the:

A) normal distribution.
B) student t-distribution.
C) F-distribution.
D) Poisson distribution.

Question 31

A survey will be conducted to compare the United Way contributions made by sales people from three county retail corporations.Sales people are to be randomly selected from each of the three corporations and the dollar amounts of their contribution recorded.The ANOVA model most likely to fit this situation is the:

A) one-way analysis of variance.
B) randomized block design.
C) two-way analysis of variance.
D) simple regression model.
E) multiple regression model.

Question 32

The F-statistic in a one-way ANOVA represents the:

A) variation between the treatments plus the variation within the treatments.
B) variation within the treatments minus the variation between the treatments.
C) variation between the treatments divided by the variation within the treatments.
D) variation within the treatments divided by the variation between the treatments.

Question 33

In using the ANOVA models,the assumptions made about the data are:

A) the samples are independent.
B) the population variances are equal.
C) the population distributions are normal.
D) A,B,and C are all assumptions made about the data.
E) the samples are dependent.

Question 34

The variation that reflects the random error from the sampling process is known as the

A) variation within the groups.
B) variation between the groups.
C) treatment mean square.
D) interaction effect.
E) treatment sum of squares.

Question 35

The one-way ANOVA model assumes that each individual observation is considered to be the sum of the overall population mean for all the treatments plus the effect of the treatment plus

A) the effect of the block.
B) the effect of the interaction.
C) the effect of the level.
D) the random error associated with the sampling process.

Question 36

In one-way ANOVA,suppose that there are five treatments with n₁ = n₂ = n₃ = 5,and n₄ = n₅ = 7.Then the mean square for error,MSE,equals:

A) SSE / 4.
B) SSE / 29.
C) SSE / 24.
D) SSE / 5.

Question 37

The variation that reflects the effect of the factor levels is known as the

A) variation within the groups.
B) variation between the groups.
C) error mean square.
D) sampling error.
E) interaction effect.

Question 38

In employing the randomized block design,the expected effect is to:

A) increase the treatment sum of squares (SSTR).
B) reduce the error sum of squares (SSE).
C) improve the significance of any differences within the treatment groups.
D) reduce the total sum of squares (SST).
E) increase the error sum of squares (SSE).

Question 39

One-way ANOVA is performed on independent samples taken from three normally distributed populations with equal variances.The following summary statistics were calculated: $$\begin{array} { l l l } n _ { 1 } = 6 & \bar { x } _ { 1 } = 50 & s _ { 1 } = 5.2 \\n _ { 2 } = 8 & \bar { x } _ { 2 } = 55 & s _ { 2 } = 4.9 \\n _ { 3 } = 6 & \bar { x } _ { 3 } = 51 & s _ { 3 } = 5.4\end{array}$$ The grand mean equals:

A) 50.0.
B) 52.0.
C) 52.3.
D) 53.0.

Question 40

One-way ANOVA is performed on three independent samples with n₁ = 6,n₂ = 7,and n₃ = 8.The critical value obtained from the F-table for this test at the 2.5% level of significance equals:

A) 3.55.
B) 39.45.
C) 4.56.
D) 29.45.

Question 41

NARRBEGIN: Annuity
A large annuity company holds many industry group stocks.Among the industries are banks,business services and construction.Seven companies from each industry group are randomly sampled to test the hypothesis that the mean price per share is the same among industries.The data are:
Compute the mean square error (MSE).

Question 42

NARRBEGIN: Annuity
A large annuity company holds many industry group stocks.Among the industries are banks,business services and construction.Seven companies from each industry group are randomly sampled to test the hypothesis that the mean price per share is the same among industries.The data are:
Compute the mean square for the between-group variation (MSTR).

Question 43

NARRBEGIN: Alumni clubs
Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city:
Calculate the error mean squares (MSE).

Question 44

A randomized block design ANOVA has five treatments and four blocks.The computed test statistic (value of F)is 4.35.With a 0.05 significance level,the appropriate table value and conclusion will be:

A) 14.37: accept the null hypothesis.
B) 3.11: accept the null hypothesis.
C) 3.26: accept the null hypothesis.
D) 2.87: reject the null hypothesis.
E) 3.26: reject the null hypothesis.

Question 45

A randomized block experiment having five treatments and six blocks produced the following values: SSTR = 287, SST = 1,446, SSE = 180. The value of SSB must be:

A) 30.
B) 979.
C) 467.
D) 20.
E) 107.

Question 46

NARRBEGIN: Alumni clubs
Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city:
What is the number of the error degrees of freedom?

Question 47

NARRBEGIN: Alumni clubs
Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city:
Calculate the total sum of squares (SST).

Question 48

The F-test of the randomized block design of the analysis of variance requires that the random variable of interest must be normally distributed and the population variances must be equal.When the random variable is not normally distributed,we can use:

A) one-way ANOVA.
B) two-way ANOVA.
C) Friedman test.
D) all of these.

Question 49

NARRBEGIN: Alumni clubs
Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city:
Compute the appropriate table value to use as the critical value at the 5% significance level.

Question 50

Three tennis players,a beginner,an intermediate,and advanced,have been randomly selected from the membership of a racquet facility club in a large city.Using the same tennis ball,each player hits ten serves,one with each of three racquet models,with the three racquet models selected randomly.The speed of each serve is measured with a machine and the result recorded.Among the ANOVA models listed below,the most likely model to fit this situation is the:

A) one-way ANOVA.
B) two-way ANOVA.
C) randomized block design.
D) none of these.

Question 51

When the effect of a level for one factor depends on which level of the other factor is present,use:

A) one-way analysis of variance.
B) randomized block design.
C) two-way analysis of variance.
D) simple regression model.
E) paired sample model.

Question 52

NARRBEGIN: Alumni clubs
Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city:
Calculate the error sum of squares (SSE).

Question 53

The equation: SST = SSA + SSB + SSAB + SSE,applies to which ANOVA model?

A) One-way ANOVA
B) Two-way ANOVA
C) Randomized block design
D) All of these

Question 54

NARRBEGIN: Grocery store
Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were:
Calculate the treatment sum of squares (SSTR).

Question 55

NARRBEGIN: Annuity
A large annuity company holds many industry group stocks.Among the industries are banks,business services and construction.Seven companies from each industry group are randomly sampled to test the hypothesis that the mean price per share is the same among industries.The data are:
Compute the appropriate table value to use as the critical value at the 2.5% significance level.

Question 56

Which of the following statements are not true regarding the randomized block design?

A) In this design,persons or test units are first arranged into similar groups,or blocks,then the treatments are randomly assigned.
B) Blocking helps reduce error variation by ensuring that the treatment groups are comparable in terms of the blocking variable.
C) This design assumes that interactions exist between the blocks and the treatments.
D) Although the blocking variable can be viewed as representing a second independent variable,it is introduced solely for the purpose of controlling error variation.
E) All of these statements are true.

Question 57

NARRBEGIN: Grocery store
Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were:
Calculate the total sum of squares (SST).

Question 58

The randomized block design with two treatments is equivalent to a non-directional:

A) independent samples z-test.
B) independent samples t-test.
C) dependent samples z-test.
D) dependent samples t-test.
E) chi-square test for independence.

Question 59

NARRBEGIN: Alumni clubs
Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city:
What is the number of the treatment degrees of freedom?

Question 60

NARRBEGIN: Alumni clubs
Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city:
Calculate the treatment sum of squares (SSTR).

Question 61

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What are the degrees of freedom for the error sum of squares?

Question 62

NARRBEGIN: Grocery store
Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were:
What is the number of the error degrees of freedom?

Question 63

NARRBEGIN: Grocery store
Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were:
Calculate the error mean squares (MSE).

Question 64

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What is the computed value for the total sum of squares (SST)?

Question 65

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What is the computed value for the sum of squares for the interaction between Factor A and Factor B (SSAB)?

Question 66

NARRBEGIN: Shelf Level
Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are:
Compute the error sum of squares (SSE).

Question 67

NARRBEGIN: Shelf Level
Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are:
Compute the sum of squares for blocks (SSB).

Question 68

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What is the computed value for Factor B (music)mean square (MSB)?

Question 69

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What is the computed value for Factor A (assembly method)sum of squares (SSA)?

Question 70

NARRBEGIN: Grocery store
Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were:
What is the number of the treatment degrees of freedom?

Question 71

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What is the computed value for Factor A (assembly method)mean square (MSA)?

Question 72

NARRBEGIN: Shelf Level
Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are:
Compute the sum of squares for treatments (SSTR).

Question 73

NARRBEGIN: Shelf Level
Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are:
Compute the error mean squares (MSE).

Question 74

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What is the computed value for the error sum of squares (SSE)?

Question 75

NARRBEGIN: Grocery store
Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were:
Compute the appropriate table value to use as the critical value at the 5% significance level.

Question 76

NARRBEGIN: Shelf Level
Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are:
Compute the total sum of squares (SST).

Question 77

NARRBEGIN: Music
A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results:
What is the computed value for Factor B (music)sum of squares (SSB)?

Question 78

NARRBEGIN: Grocery store
Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were:
Calculate the error sum of squares (SSE).

Question 79

NARRBEGIN: Shelf Level
Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are:
Compute the mean squares for treatments (MSTR).

Question 80

NARRBEGIN: Shelf Level
Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are:
Compute the mean squares for blocks (MSB).