Deck 13: Experimental Design and Analysis of Variance

Question 1

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

A) 3.74
B) 2.25
C) 2.37
D) 1.96

Answer 1

2.25

Question 2

In an analysis of variance problem involving three treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is _____.

A) 133.2
B) 13.32
C) 14.8
D) 30.0

Answer 2

14.8

Question 3

In the ANOVA, treatment refers to _____.

A) experimental units
B) different levels of a factor
C) a factor
D) applying antibiotic to a wound

Answer 3

different levels of a factor

Question 4

When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is _____.

A) SSTR/nT
B) SSTR/(nT - 1)
C) SSTR/k
D) SSTR/(k - 1)

Question 5

In ANOVA, which of the following is NOT affected by whether or not the population means are equal?

A) $\bar{x}$
B) between-samples estimate of $\sigma$ ²
C) within-samples estimate of $\sigma$ ²
D) None of the answers is correct.

Question 6

The F ratio in a completely randomized ANOVA is the ratio of _____.

A) MSTR/MSE
B) MST/MSE
C) MSE/MSTR
D) MSE/MST

Question 7

An ANOVA procedure is used for data that were obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are _____.

A) 3 and 20
B) 3 and 16
C) 4 and 17
D) 3 and 19

Question 8

In the analysis of variance procedure (ANOVA), factor refers to _____.

A) the dependent variable
B) the independent variable
C) different levels of a treatment
D) the critical value of F

Question 9

To determine whether the means of two populations are equal, _____.

A) a t test must be performed
B) an analysis of variance must be performed
C) either a t test or an analysis of variance can be performed
D) a chi-square test must be performed

Question 10

A term that means the same as the term "variable" in an ANOVA procedure is _____.

A) factor
B) treatment
C) replication
D) variance within

Question 11

In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as _____.

A) the main effect
B) replication
C) interaction
D) None of the answers is correct.

Question 12

The process of allocating the total sum of squares and degrees of freedom is called _____.

A) factoring
B) blocking
C) replicating
D) partitioning

Question 13

The required condition for using an ANOVA procedure on data from several populations is that the _____.

A) selected samples are dependent on each other
B) sampled populations are all uniform
C) sampled populations have equal variances
D) sampled populations have equal means

Question 14

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is _____.

A) SSE/(nT - k)
B) SSTR/(nT - k)
C) SSE/(k - 1)
D) SSE/k

Question 15

The mean square is the sum of squares divided by _____.

A) the total number of observations
B) its corresponding degrees of freedom
C) its corresponding degrees of freedom minus1
D) None of the answers is correct.

Question 16

The ANOVA procedure is a statistical approach for determining whether the means of _____.

A) two samples are equal
B) two or more samples are equal
C) more than two samples are equal
D) two or more populations are equal

Question 17

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

A) factor block design
B) random factor design
C) completely randomized design
D) None of the answers is correct.

Question 18

The number of times each experimental condition is observed in a factorial design is known as a(n) _____.

A) partition
B) replication
C) experimental condition
D) factor

Question 19

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are _____.

A) 6 numerator and 20 denominator degrees of freedom
B) 5 numerator and 20 denominator degrees of freedom
C) 5 numerator and 114 denominator degrees of freedom

Question 20

The independent variable of interest in an ANOVA procedure is called _____.

A) a partition
B) a treatment
C) either a partition or a treatment
D) a factor

Question 21

In an analysis of variance, one estimate of $\sigma$ is based upon the differences between the treatment means and the _____.

A) means of each sample
B) overall sample mean
C) sum of observations
D) populations have equal means

Question 22

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = .01 is _____.

A) 2.28
B) 3.20
C) 3.33
D) 3.64

Question 23

Random samples were selected from three populations. The data obtained are shown below. At a 5% level of significance, test to see if there is a significant difference in the means of the three populations. (Please note that the sample sizes are not equal.)

Question 24

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____.

A) 5 and 20
B) 4 and 20
C) 4 and 99
D) 4 and 95

Question 25

Three different models of automobiles (A, B, and C) were compared for gasoline consumption. For each model of car, fifteen cars were randomly selected and subjected to standard driving procedures. The average miles/gallon obtained for each model of car and sample standard deviations are shown below. Use the above data and test to see if the mean gasoline consumption for all three models of cars is the same. Let α = .05.
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Question 26

Which of the following is NOT a required assumption for the analysis of variance?

A) The random variable of interest for each population has a normal probability distribution.
B) The variance associated with the random variable must be the same for each population.
C) At least two populations are under consideration.
D) Populations have equal means.

Question 27

Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology. From each institution, a random sample of MS recipients was selected, and these recipients were then given the exam. The following table shows the scores of the students from each university. At α = .01, test to see if there is any significant difference in the average scores of the students from the three universities. (Note that the sample sizes are not equal.)
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Question 28

The test scores for selected samples of sociology students who took the course from three different instructors are shown below. At α = .05, test to see if there is a significant difference among the averages of the three groups.
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Question 29

Six observations were selected from each of three populations. The data obtained are shown below. Test at α = .05 level to determine if there is a significant difference in the means of the three populations.
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Question 30

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____.

A) 3 and 30
B) 4 and 30
C) 3 and 119
D) 3 and 116

Question 31

In a completely randomized design involving three treatments, the following information is provided: Treatment 1
$\begin{array} { l } & \text {Treatment 1 }& \text {Treatment 2 }& \text {Treatment 3 }\\\hline \text {Sample size }&5&10&5\\\text { Sample mean }&4&8&9\\\end{array}$

?
The overall mean for all the treatments is ______.

A) 7.00
B) 6.67
C) 7.25
D) 4.89

Question 32

The manager of Young Corporation wants to determine whether or not the type of work schedule for her employees has any effect on their productivity. She has selected 15 production employees at random and then randomly assigned five employees to each of the three proposed work schedules. The following table shows the units of production (per week) under each of the work schedules. At a 5% level of significance, determine if there is a significant difference in the mean weekly units of production for the three types of work schedules.

Question 33

Three different brands of tires were compared for wear characteristics. For each brand of tire, 10 tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations (both in 1000 miles) are shown below. Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let α = .05.

Question 34

In a completely randomized design involving four treatments, the following information is provided. $\begin{array} { l } & \text {Treatment 1 }& \text {Treatment 2 }& \text {Treatment 3 }& \text {Treatment 4 }\\\hline \text {Sample size }&50&18&15&17\\\text { Sample mean }&32&38&42&48\\\end{array}$
The overall mean (the grand mean) for all treatments is _____.

A) 40.0
B) 37.3
C) 48.0
D) 37.0
E) None of the answers is correct.

Question 35

MNM, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (in $1,000s) are shown below. At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. Show your complete work and the ANOVA table. (Please note that the sample sizes are not equal.)
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Question 36

Guitars R. US has three stores located in three different areas. Random samples of the sales of the three stores (in $1000) are shown below: At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. (Please note that the sample sizes are not equal.)

Question 37

Random samples were selected from three populations. The data obtained are shown below. At a 5% level of significance, test to see if there is a significant difference in the means of the three populations. (Please note that the sample sizes are not equal.)
​

Question 38

If we are testing for the equality of 3 population means, we should use the _____.

A) test statistic F
B) test statistic t
C) test statistic z
D) test statistic χ2

Question 39

In testing for the equality of k population means, the number of treatments is _____.

A) k
B) k-1
C) nT
D) nT - k

Question 40

An experimental design that permits statistical conclusions about two or more factors is a _____.

A) randomized block design
B) factorial design
C) completely randomized design
D) randomized design

Question 41

The final examination grades of random samples of students from three different classes are shown below. At the α = .05 level of significance, is there any difference in the mean grades of the three classes?

Question 42

A factorial experiment involving two levels of factor A and two levels of factor B resulted in the following. Set up the ANOVA table and test for any significant main effect and any interaction effect. Use α = .05.

Question 43

In a completely randomized experimental design, 11 experimental units were used for each of the four treatments. Part of the ANOVA table is shown below. Fill in the blanks in the above ANOVA table.
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Question 44

Halls, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (in $1,000s) are shown below. At a 5% level of significance, use Excel to determine whether there is a significant difference in the average sales of the three stores.

Question 45

Eight observations were selected from each of three populations, and an analysis of variance was performed on the data. The following are the results: ​
Using α = .05, test to see if there is a significant difference among the means of the three populations. The sample sizes for the three treatments are equal.

Question 46

Random samples of individuals from three different cities were asked how much time they spend per day watching television. The results (in minutes) for the three groups are shown below. At α = .05, test to see if there is a significant difference in the averages of the three groups.

Question 47

Three universities in your state decided to administer the same comprehensive examination to the recipients of MBA degrees from the three institutions. From each institution, MBA recipients were randomly selected and were given the test. The following table shows the scores of the students from each university. At α = .01, test to see if there is any significant difference in the average scores of the students from the three universities. (Note that the sample sizes are not equal.)

Question 48

Random samples of employees from three different departments of MNM Corporation showed the following yearly incomes (in $1,000s). At α = .05, test to determine if there is a significant difference among the average incomes of the employees from the three departments.

Question 49

Five drivers were selected to test drive two makes of automobiles. The following table shows the number of miles per gallon for each driver driving each car. Consider the makes of automobiles as treatments and the drivers as blocks and test to see if there is any difference in the miles/gallon of the two makes of automobiles. Let α = .05.

Question 50

MNM, Inc. has three stores located in three different areas. Random samples of the daily sales of the three stores (in $1,000s) are shown below. At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores.
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Question 51

Halls, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (In $1,000s) are shown below. At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores.

Question 52

Three different brands of tires were compared for wear characteristics. From each brand of tire, 10 tires were randomly selected and subjected to standard wear-testing procedures. The average mileage obtained for each brand of tire and sample variances (both in 1,000 miles) are shown below. Using α = .05, test to see if there is a significant difference in the average mileage of the three tires.
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Question 53

Three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds of the tested cars are given below. At α = .05, test to see if there is a significant difference in the average speeds of the cars of the auto manufacturers.

Question 54

To test to determine whether there is any significant difference in the mean number of units produced per week by each of three production methods, the following data were collected: At the α = .05 level of significance, is there any difference in the mean number of units produced per week by each method? Show the complete ANOVA table. (Please note that the sample sizes are not equal.)

Question 55

For four populations, the population variances are assumed to be equal. Random samples from each population provide the following data. Using a .05 level of significance, test to see if the means for all four populations are the same.

Question 56

The heating bills for a selected sample of houses using various forms of heating are given below (values are in dollars). At α = .05, test to see if there is a significant difference among the average bills of the homes.

Question 57

Individuals were randomly assigned to three different production processes. The hourly units of production for the three processes are shown below. ​
Use the analysis of variance procedure with α = .05 to determine if there is a significant difference in the mean hourly units of production for the three types of production processes.

Question 58

Samples were selected from three populations. The data obtained are shown below. At a 5% level of significance, use Excel to test to determine whether there is a significant difference in the means of the three populations.

Question 59

At α = .05, test to determine if the means of the three populations (from which the following samples are selected) are equal.

Question 60

In a completely randomized experimental design, 14 experimental units were used for each of the five levels of the factor (i.e., five treatments). Fill in the blanks in the following ANOVA table. ​

Question 61

Employees of MNM Corporation are about to undergo a retraining program. Management is trying to determine which of three programs is the best. They believe that the effectiveness of the programs may be influenced by gender. A factorial experiment was designed. You are given the following information. What advice would you give MNM? Use Excel and a .05 level of significance.

Question 62

The independent variable of interest in an ANOVA procedure is called _____.

A) a partition
B) a treatment
C) either a partition or a treatment
D) a factor

Question 63

To test whether the time required to fully load a standard delivery truck is the same for three work shifts (day, evening, and night), NatEx obtained the following data on the time (in minutes) needed to pack a truck. Use these data to test whether the population mean times for loading a truck differ for the three work shifts. Use α = .05.
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Question 64

Five drivers were selected to test drive two makes of automobiles. The following table shows the number of miles per gallon for each driver driving each car. Consider the makes of automobiles as treatments and the drivers as blocks and use Excel to determine whether there is any difference in the miles/gallon of the two makes of automobiles. Let α = .05.

Question 65

A factorial experiment involving two levels of factor A and two levels of factor B resulted in the following. Use Excel and test for any significant main effect and any interaction effect. Use α = .05.

Question 66

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are _____.

A) 6 numerator and 20 denominator degrees of freedom
B) 5 numerator and 20 denominator degrees of freedom
C) 5 numerator and 114 denominator degrees of freedom

Question 67

The F ratio in a completely randomized ANOVA is the ratio of _____.

A) MSTR/MSE
B) MST/MSE
C) MSE/MSTR
D) MSE/MST

Question 68

In the ANOVA, treatment refers to _____.

A) experimental units
B) different levels of a factor
C) a factor
D) applying antibiotic to a wound

Question 69

Three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds of the tested cars are given below. At α = .05, use Excel to determine whether there is a significant difference in the average speeds of the cars of the auto manufacturers.

Question 70

In an analysis of variance problem involving three treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is _____.

A) 133.2
B) 13.32
C) 14.8
D) 30.0

Question 71

In an analysis of variance problem, if SST = 120 and SSTR = 80, then SSE is _____.

A) 200
B) 40
C) 80
D) 120

Question 72

Random samples of individuals from three different cities were asked how much time they spend per day watching television. The results (in minutes) for the three groups are shown below. At α = .05, use Excel to test to see if there is a significant difference in the averages of the three groups.

Question 73

A research organization wishes to determine whether four brands of batteries for transistor radios perform equally well. Three batteries of each type were randomly selected and installed in the three test radios. The number of hours of use for each battery is given below. Consider the three different test radios and use Excel to carry out the analysis of variance procedure for a randomized block design. Use a .05 level of significance.

Question 74

A dietitian wants to see if there is any difference in the effectiveness of three diets. Eighteen people, comprising a sample, were randomly assigned to the three diets. Below you are given the total amount of weight lost in a month by each person. What would you advise the dietician about the effectiveness of the three diets? Use Excel and a .05 level of significance.
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Question 75

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is _____.

A) SSE/(nT - k)
B) SSTR/(nT - k)
C) SSE/(k - 1)
D) SSE/k

Question 76

In the analysis of variance procedure (ANOVA), factor refers to _____.

A) the dependent variable
B) the independent variable
C) different levels of a treatment
D) the critical value of F

Question 77

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

A) 3.74
B) 2.25
C) 2.37
D) 1.96

Question 78

Individuals were randomly assigned to three different production processes. The hourly units of production for the three processes are shown below. Use Excel with α = .05 to determine whether there is a significant difference in the mean hourly units of production for the three types of production processes.

Question 79

When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is _____.

A) SSTR/nT
B) SSTR/(nT - 1)
C) SSTR/k
D) SSTR/(k - 1)

Question 80

The ANOVA procedure is a statistical approach for determining whether the means of _____.

A) two samples are equal
B) two or more samples are equal
C) more than two samples are equal
D) two or more populations are equal