# Quiz 14: Analysis of Variance

Statistics

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Q 4Q 4

The sum of squares for treatments, SST, achieves its smallest value (zero) when all the sample means are equal.

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Q 5Q 5

The analysis of variance (ANOVA) technique analyzes the variance of the data to determine whether differences exist between the population means.

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Q 6Q 6

Conducting t-tests for each pair or population means is statistically equivalent to conducting one F-test comparing all the population means.

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Q 8Q 8

In one-way ANOVA, the total variation SS(Total) is partitioned into two sources of variation: the sum of squares for treatments (SST) and the sum of squares for error (SSE).

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Q 10Q 10

In one-way ANOVA, the test statistic is defined as the ratio of the mean square for error (MSE) and the mean square for treatments (MST), namely, F = MSE / MST.

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Q 11Q 11

The F-statistic in a one-way ANOVA represents the variation within the treatments divided by the variation between the treatments.

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Q 13Q 13

The sum of squares for treatments (SST) is the variation attributed to the differences between the treatment means, while the sum of squares for error (SSE) measures the within-treatment variation.

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Q 14Q 14

If the numerator (MST) degrees of freedom is 3 and the denominator (MSE) degrees of freedom is 18, the total number of observations must equal 21.

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Q 15Q 15

The sum of squares for error (SSE) measures the amount of variation that is explained by the ANOVA model, while the sum of squares for treatments (SST) measures the amount of variation that remains unexplained.

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Q 16Q 16

The analysis of variance (ANOVA) tests hypotheses about population variances and requires all the population means to be equal.

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Q 19Q 19

The within-treatments variation provides a measure of the amount of variation in the response variables that is caused by the treatments.

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Q 21Q 21

The test statistic of the single-factor ANOVA equals:
A) sum of squares for treatments / sum of squares for error.
B) sum of squares for error / sum of squares for treatments.
C) mean square for treatments / mean square for error.
D) mean square for error / mean square for treatments.

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Multiple Choice

Q 22Q 22

In a single-factor analysis of variance, MST is the mean square for treatments and MSE is the mean square for error.The null hypothesis of equal population means is rejected if:
A) MST is much larger than MSE.
B) MST is much smaller than MSE.
C) MST is equal to MSE.
D) None of these choices.

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Multiple Choice

Q 23Q 23

In one-way ANOVA, the amount of total variation that is unexplained is measured by the:
A) sum of squares for treatments.
B) degrees of freedom.
C) total sum of squares.
D) sum of squares for error.

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Q 24Q 24

In a one-way ANOVA, error variability is computed as the sum of the squared errors, SSE, for all values of the response variable.This variability is the:
A) the total variation.
B) within-treatments variation.
C) between-treatments variation.
D) None of these choices.

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Multiple Choice

Q 25Q 25

Which of the following is not a required condition for one-way ANOVA?
A) The sample sizes must be equal.
B) The populations must all be normally distributed.
C) The population variances must be equal.
D) The samples for each treatment must be selected randomly and independently.

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Q 26Q 26

The analysis of variance is a procedure that allows statisticians to compare two or more population:
A) proportions.
B) means.
C) variances.
D) standard deviations.

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Q 27Q 27

The distribution of the test statistic for analysis of variance is the:
A) normal distribution.
B) Student t-distribution.
C) F-distribution.
D) None of these choices.

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Multiple Choice

Q 28Q 28

In the one-way ANOVA where there are k treatments and n observations, the degrees of freedom for the F-statistic are equal to, respectively:
A) n and k.
B) k and n.
C) n k and k 1.
D) k 1 and n k.

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Multiple Choice

Q 29Q 29

In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the degrees of freedom for treatments is given by:
A) n k
B) k 1
C) n 1
D) n k + 1

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Multiple Choice

Q 30Q 30

In ANOVA, the F-test is the ratio of two sample variances.In the one-way ANOVA (completely randomized design), the variance used as a numerator of the ratio is:
A) mean square for treatments.
B) mean square for error.
C) total sum of squares.
D) None of these choices.

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Multiple Choice

Q 31Q 31

In a completely randomized design for ANOVA, the numerator and denominator degrees of freedom are 4 and 25, respectively.The total number of observations must equal:
A) 24
B) 25
C) 29
D) 30

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Q 32Q 32

The number of degrees of freedom for the denominator in one-way ANOVA test involving 4 population means with 15 observations sampled from each population is:
A) 60
B) 19
C) 56
D) 45

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Q 33Q 33

The value of the test statistic in a completely randomized design for ANOVA is F = 6.29.The degrees of freedom for the numerator and denominator are 5 and 10, respectively.Using an F table, the most accurate statements to be made about the p-value is that it is:
A) greater than 0.05
B) between 0.001 and 0.010.
C) between 0.010 and 0.025.
D) between 0.025 and 0.050.

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Multiple Choice

Q 34Q 34

In one-way ANOVA, the term refers to the:
A) weighted average of the sample means.
B) sum of the sample means divided by the total number of observations.
C) sum of the population means.
D) sum of the sample means.

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Multiple Choice

Q 35Q 35

Which of the following is a required condition for ANOVA?
A) The populations are normally distributed.
B) The population variances are equal.
C) The samples are independent.
D) All of these choices are required conditions for ANOVA.

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Multiple Choice

Q 36Q 36

In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the number of degrees of freedom for error is:
A) k 1
B) n 1
C) n k
D) n k + 1

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Multiple Choice

Q 37Q 37

One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances.Which of the following is the null hypothesis for this procedure?
A)

_{1}+ _{2}+ _{3}= 0 B) _{1}+ _{2}+ _{3} 0 C) _{1}= _{2}= _{3}= 0 D) _{1}= _{2}= _{3}Free

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Q 38Q 38

How does conducting multiple t-tests compare to conducting a single F-test?
A) Multiple t-tests increases the chance of a Type I error.
B) Multiple t-tests decreases the chance of a Type I error.
C) Multiple t-tests does not affect the chance of a Type I error.
D) This comparison cannot be made without knowing the number of populations.

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Multiple Choice

Q 39Q 39

In one-way analysis of variance, between-treatments variation is measured by the:
A) SSE
B) SS(Total)
C) SST
D) standard deviation

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Multiple Choice

Q 40Q 40

One-way ANOVA is applied to independent samples taken from four normally distributed populations with equal variances.If the null hypothesis is rejected, then we can infer that
A) all population means are equal.
B) all population means differ.
C) at least two population means are equal.
D) at least two population means differ.

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Multiple Choice

Q 41Q 41

Consider the following partial ANOVA table: The numerator and denominator degrees of freedom for the F-test (identified by asterisks) are
A) 4 and 15
B) 3 and 16
C) 15 and 4
D) 16 and 3

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Q 43Q 43

In one-way analysis of variance, within-treatments variation is measured by:
A) sum of squares for error.
B) sum of squares for treatments.
C) total sum of squares.
D) standard deviation.

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Multiple Choice

Q 44Q 44

Consider the following ANOVA table: The total number of observations is:
A) 25
B) 29
C) 30
D) 32

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Multiple Choice

Q 45Q 45

In one-way analysis of variance, if all the sample means are equal, then the:
A) total sum of squares is zero.
B) sum of squares for treatments is zero.
C) sum of squares for error is zero.
D) sum of squares for error equals sum of squares for treatments.

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Multiple Choice

Q 46Q 46

Which of the following components in an ANOVA table is not additive?
A) Sum of squares
B) Degrees of freedom
C) Mean squares
D) All of these choices are additive.

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Q 47Q 47

In which case can an F-test be used to compare two population means?
A) For one tail tests only.
B) For two tail tests only.
C) For either one or two tail tests.
D) None of these choices.

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Multiple Choice

Q 48Q 48

The F-test statistic in a one-way ANOVA is equal to:
A) MST/MSE
B) SST/SSE
C) MSE/MST
D) SSE/SST

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Multiple Choice

Q 49Q 49

The numerator and denominator degrees of freedom for the F-test in a one-way ANOVA are, respectively,
A) (n k) and (k 1)
B) (k 1) and (n k)
C) (k n) and (n 1)
D) (n 1) and (k n)

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Multiple Choice

Q 50Q 50

Which of the following statements is true?
A) F = t

^{2}B) The F-test can be used instead of a two tail t-test when you compare two population means. C) Doing three t-tests is statistically equivalent to doing one F-test when you compare three population means. D) All of these choices are true.Free

Multiple Choice

Q 51Q 51

The ANOVA procedure tests to determine whether differences exist between two or more population ____________________.

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Q 53Q 53

The alternative hypothesis of ANOVA is that ____________________ population means are different.

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Q 54Q 54

In ANOVA the populations are classified according to one or more criterion, called ____________________.

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Q 57Q 57

The F-test statistic in ANOVA is equal to MS____________________ divided by MS____________________ and H

_{0}is rejected for ____________________ values of F.Free

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Q 58Q 58

If SST explains a significant portion of the total variation, we conclude that the population means ____________________ (do/do not) differ.

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Q 59Q 59

The F-test in ANOVA requires that the random variable be ____________________ distributed with equal ____________________.

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Q 60Q 60

If we square the t-statistic for two means, the result is the ____________________-statistic.

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Q 61Q 61

TV News Viewing Habits
A statistician employed by a television rating service wanted to determine if there were differences in television viewing habits among three different cities in New York.She took a random sample of five adults in each of the cities and asked each to report the number of hours spent watching television in the previous week.The results are shown below.(Assume normal distributions with equal variances.)
-{TV News Viewing Habits Narrative} Set up the ANOVA Table.Use = 0.05 to determine the critical value.

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Q 62Q 62

TV News Viewing Habits
A statistician employed by a television rating service wanted to determine if there were differences in television viewing habits among three different cities in New York.She took a random sample of five adults in each of the cities and asked each to report the number of hours spent watching television in the previous week.The results are shown below.(Assume normal distributions with equal variances.)
-{TV News Viewing Habits Narrative} Can she infer at the 5% significance level that differences in hours of television watching exist among the three cities?

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Q 63Q 63

Arthritis Pain Formulas
A pharmaceutical manufacturer has been researching new medications formulas to provide quicker relief of arthritis pain.Their laboratories have produced three different medications and they want to determine if the different medications produce different responses.Fifteen people who complained of arthritis pains were recruited for an experiment; five were randomly assigned to each medication.Each person was asked to take the medicine and report the length of time until some relief was felt (minutes).The results are shown below.(Assume normal distributions with equal variances.)
-{Arthritis Pain Formulas Narrative} Set up the ANOVA Table.Use = 0.05 to determine the critical value.

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Q 64Q 64

Arthritis Pain Formulas
A pharmaceutical manufacturer has been researching new medications formulas to provide quicker relief of arthritis pain.Their laboratories have produced three different medications and they want to determine if the different medications produce different responses.Fifteen people who complained of arthritis pains were recruited for an experiment; five were randomly assigned to each medication.Each person was asked to take the medicine and report the length of time until some relief was felt (minutes).The results are shown below.(Assume normal distributions with equal variances.)
-{Arthritis Pain Formulas Narrative} Do these data provide sufficient evidence to indicate that differences in the average time of relief exist among the three medications? Use = 0.05.

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Q 65Q 65

Sub Sandwich Customers
The marketing manager of a Sub Shop chain is in the process of examining some of the demographic characteristics of her customers.In particular, she would like to investigate the belief that the ages of the customers of Sub Shops, hamburger emporiums, and fast-food chicken restaurants are different.The ages of eight randomly selected customers of each of the restaurants are recorded and listed below.From previous analyses we know that the ages are normally distributed with equal variances for each group.
-{Sub Sandwich Customers Narrative} Set up the ANOVA Table.Use = 0.05 to determine the critical value.

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Q 66Q 66

Sub Sandwich Customers
The marketing manager of a Sub Shop chain is in the process of examining some of the demographic characteristics of her customers.In particular, she would like to investigate the belief that the ages of the customers of Sub Shops, hamburger emporiums, and fast-food chicken restaurants are different.The ages of eight randomly selected customers of each of the restaurants are recorded and listed below.From previous analyses we know that the ages are normally distributed with equal variances for each group.
-{Sub Sandwich Customers Narrative} Do these data provide enough evidence at the 5% significance level to infer that there are differences in ages among the customers of the three restaurants?

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Q 67Q 67

GMAT Scores
A recent college graduate is in the process of deciding which one of three graduate schools he should apply to.He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school.A random sample of six students in each school produced the following GMAT scores.Assume that the data are normally distributed with equal variances for each school.
-{GMAT Scores Narrative} Set up the ANOVA Table.Use = 0.05 to determine the critical value.

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Q 68Q 68

GMAT Scores
A recent college graduate is in the process of deciding which one of three graduate schools he should apply to.He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school.A random sample of six students in each school produced the following GMAT scores.Assume that the data are normally distributed with equal variances for each school.
-{GMAT Scores Narrative} Can he infer at the 10% significance level that the GMAT scores differ among the three schools?

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Q 69Q 69

In a completely randomized design, 15 experimental units were assigned to each of four treatments.Fill in the blanks (identified by asterisks) in the partial ANOVA table shown below.

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Q 70Q 70

Gold Funds
An investor studied the percentage rates of return of three different gold funds.Random samples of percentage rates of return for four periods were taken from each fund.The results appear in the table below:
-{Gold Funds Narrative} Set up the ANOVA Table.Use = 0.05 to determine the critical value.

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Q 71Q 71

Gold Funds
An investor studied the percentage rates of return of three different gold funds.Random samples of percentage rates of return for four periods were taken from each fund.The results appear in the table below:
-{Gold Funds Narrative} Test at the 5% significance level to determine whether the mean percentage rates for the three funds differ.

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Q 72Q 72

The Bonferroni adjustment to Fisher's Least Significant Difference (LSD) multiple comparison method is made by dividing the specified experimentwise Type I error rate by the number of pairs of population means.

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Q 73Q 73

The Bonferroni adjustment decreases the experimentwise Type I error rate, but it increases the probability of a Type II error.

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Q 74Q 74

Multiple comparison methods are used to determine whether or not any differences occur amongst a group of population means.

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Q 75Q 75

Fisher's least significant difference method (LSD) substitutes the pooled variance estimator from the equal variances t-test with the MSE from ANOVA.

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Q 76Q 76

Tukey's multiple comparison method is more powerful than Fisher's LSD Method at finding differences in pairwise population means.

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Q 78Q 78

In Fisher's least significant difference (LSD) multiple comparison method, the LSD value will be the same for all pairs of means if:
A) all sample sizes are the same.
B) all sample means are the same.
C) all population means are the same.
D) None of these choices.

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Multiple Choice

Q 79Q 79

Fisher's least significant difference (LSD) multiple comparison method is flawed because
A) it will increase ; the probability of committing a Type II error
B) it will increase ; the probability of committing a Type I error
C) it will increase both and , the probabilities of committing Type I and Type II errors, respectively.
D) None of these choices.

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Multiple Choice

Q 80Q 80

Which of the following statements about multiple comparison methods is false?
A) They are to be use once the F-test in ANOVA has been rejected.
B) They are used to determine which particular population means differ.
C) There are many different multiple comparison methods but all yield the same conclusions.
D) All of these choices are true.

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Multiple Choice

Q 81Q 81

Which of the following is true of Tukey's Multiple Comparison Method?
A) It is based on the studentized range statistic to obtain the critical value needed to construct individual confidence intervals.
B) It theoretically requires that all sample sizes be equal, or at least similar.
C) It is more powerful than the LSD method.
D) All of these choices are true.

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Multiple Choice

Q 82Q 82

When is the Tukey multiple comparison method used?
A) To test for normality.
B) To test for differences in pairwise means.
C) To test for equality of a group of population means.
D) To test equal variances.

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Multiple Choice

Q 83Q 83

The techniques used to detect which population means differ are called multiple ____________________ methods.

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Q 84Q 84

Multiple comparison methods are used after it is found that H

_{0}from ANOVA has been ____________________.Free

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Q 85Q 85

The ____________________ adjustment used with the LSD method decreases the experimentwise Type I error rate.

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Q 86Q 86

Tukey's multiple comparison method is ____________________ (more/less) powerful than Fisher's LSD method.

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Q 87Q 87

____________________ multiple comparison method is based on the Studentized range statistic.

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Q 88Q 88

If you plan to compare all possible combinations of pairs of population means, the multiple comparison method to use is ____________________ method.

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Q 89Q 89

Health Inspectors' Ages
In order to examine the differences in ages of health inspectors among five counties, a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties.
-{Health Inspectors' Ages Narrative} Use Tukey's multiple comparison method to determine which means differ.

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Q 90Q 90

Health Inspectors' Ages
In order to examine the differences in ages of health inspectors among five counties, a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties.
-{Health Inspectors' Ages Narrative} Use Fisher's LSD procedure with = .05 to determine which population means differ.

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Q 91Q 91

Health Inspectors' Ages
In order to examine the differences in ages of health inspectors among five counties, a Health Department statistician took random samples of six inspectors' ages in each county.The data are listed below.An F-test using ANOVA showed that average age differs for at least two counties.
-{Health Inspectors' Ages Narrative} Did Tukey's method and Fisher's LSD method in the previous two questions yield the same results? Will this always be the case?

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Q 92Q 92

LSAT Scores
A recent college graduate is in the process of deciding which one of three Law schools he should apply to.He decides to judge the quality of the schools on the basis of the Law School Admission Test (LSAT) scores of those who are accepted into the school.A random sample of six students in each school produced the following LSAT scores.An F-test using ANOVA concluded that average LSAT scores differ for at least two of the schools.
-{LSAT Scores Narrative} Use Fisher's LSD method with = 0.05 to determine which school's means differ.

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Q 93Q 93

LSAT Scores
A recent college graduate is in the process of deciding which one of three Law schools he should apply to.He decides to judge the quality of the schools on the basis of the Law School Admission Test (LSAT) scores of those who are accepted into the school.A random sample of six students in each school produced the following LSAT scores.An F-test using ANOVA concluded that average LSAT scores differ for at least two of the schools.
-{LSAT Scores Narrative} Use Tukey's method with = 0.05 to determine which population means differ.

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Q 94Q 94

The average cost of remodeling one room in a house was compared for four different remodeling companies.A random sample of 10 rooms remodeled by each company were selected all with the same square footage, and cost of remodeling each room was recorded.(Rooms were randomly chosen from different houses.) The data are shown below.An F-test using ANOVA concluded that average costs differ for at least two of the remodeling companies.
Use Tukey's and LSD multiple comparison methods to determine which remodeling companies differ in their average cost.Compare the results and discuss.(Keep the experimentwise Type I error at or close to 5%.)

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Q 95Q 95

A randomized block experiment having five treatments and six blocks produced the following values: SST = 252, SS(Total) = 1,545, SSE = 198.The value of SSB must be 1095.

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Q 96Q 96

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 2000, SST = 400, SSE = 200.The value of MSB must be 350.

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Q 97Q 97

In employing the randomized block design, the primary interest lies in reducing sum of squares for blocks (SSB).

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Q 98Q 98

When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.

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Q 99Q 99

One example of a blocking variable is the dosage level that each subject is assigned to in a randomized experiment.

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Q 100Q 100

The F-test of the randomized block design of the analysis of variance has the same requirements as the independent samples design; that is, the random variable must be normally distributed and the population variances must be equal.

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True False

Q 101Q 101

The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST) to more easily detect differences between the treatment means.

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True False

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Q 103Q 103

SSE in the independent samples design is equal to the sum of SSB and SSE in the randomized block design.

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Q 104Q 104

In the randomized block design for ANOVA, where k is the number of treatments and b is the number of blocks, the number of degrees of freedom for error is:
A) k b
B) kb 1
C) n k b + 1
D) None of these choices.

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Multiple Choice

Q 105Q 105

Which of the following statements is true?
A) A fixed-effects ANOVA refers to the analysis which includes all possible levels of a factor.
B) A random-effects ANOVA refers to the analysis where the levels included in the study represent a random sample of all levels that exist.
C) A multifactor experiment is one where there are two or more factors that define the treatments.
D) All of these choices are true.

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Multiple Choice

Q 106Q 106

In the randomized block design ANOVA, the sum of squares for error equals:
A) SS(Total) SST
B) SS(Total) SSB
C) SS(Total) SST SSB
D) None of these choices.

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Multiple Choice

Q 107Q 107

When the objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called a:
A) completely randomized design.
B) one-way ANOVA design.
C) randomized block design.
D) None of these choices.

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Multiple Choice

Q 108Q 108

The primary interest of designing a randomized block experiment is to:
A) reduce the within-treatments variation to more easily detect differences among the treatment means.
B) increase the between-treatments variation to more easily detect differences among the treatment means.
C) reduce the variation among blocks.
D) None of these choices.

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Multiple Choice

Q 109Q 109

The randomized block design with exactly two treatments is equivalent to a two-tail:
A) independent samples z-test.
B) independent samples equal-variances t-test.
C) independent samples unequal-variances t-test.
D) matched pairs t-test.

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Multiple Choice

Q 110Q 110

Which of the following is true regarding SSB?
A) SSB stands for sum of squares for blocks.
B) SSB can help to reduce SSE.
C) SSB can help make it easier to determine whether differences exist between the treatment means.
D) All of these choices are true.

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Multiple Choice

Q 111Q 111

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1,951, SST = 349, SSE = 188 .The value of SSB must be:
A) 537
B) 1,763
C) 1,414
D) 1,602

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Multiple Choice

Q 112Q 112

The F-test of a randomized block design of the analysis of variance has the same requirements as the independent samples design; that is, the random variable must be ____________________ distributed and the population ____________________ must be equal.

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Q 113Q 113

SSE in the independent samples design is equal to the sum of SS____________________ and SS____________________ in the randomized block design.

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Q 114Q 114

In employing the randomized block design, the primary interest lies in reducing sum of squares for ____________________.

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Q 115Q 115

When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called the randomized ____________________ design.

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Q 116Q 116

When we perform a blocked experiment by using the same subject for each treatment, this is called a(n) ____________________ design.

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Q 117Q 117

If our analysis includes all possible levels of a factor, the technique for analyzing the data is called a(n) ____________________-effects ANOVA.

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Q 118Q 118

The test of whether the block means differ uses an F-test whose test statistic is ____________________ divided by ____________________.

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Q 119Q 119

Motorcycle Repair Cost
Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions and estimate the cost of repairs.An insurance executive claims that there are significant differences in the estimates from different appraisers.To support his claim he takes a random sample of six motorcycles that have recently been damaged in accidents.Three appraisers then estimate the repair costs of all six motorcycles.The data are shown below.
-{Motorcycle Repair Cost Narrative} Set up the ANOVA Table.Use = 0.05 to determine the critical values.

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Q 120Q 120

Motorcycle Repair Cost
Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions and estimate the cost of repairs.An insurance executive claims that there are significant differences in the estimates from different appraisers.To support his claim he takes a random sample of six motorcycles that have recently been damaged in accidents.Three appraisers then estimate the repair costs of all six motorcycles.The data are shown below.
-{Motorcycle Repair Cost Narrative} Can we infer at the 5% significance level that the executive's claim is true?

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Q 121Q 121

Food Irradiation
In recent years the irradiation of food to reduce bacteria and preserve the food longer has become more common.A company that performs this service has developed four different methods of irradiating food.To determine which is best, it conducts an experiment where different foods are irradiated and the bacteria count is measured.As part of the experiment the following foods are irradiated: meat, poultry, veal, tuna, and yogurt.The results are shown below.
-{Food Irradiation Narrative} Set up the ANOVA Table.Use = 0.01 to determine the critical values.

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Q 122Q 122

Food Irradiation
In recent years the irradiation of food to reduce bacteria and preserve the food longer has become more common.A company that performs this service has developed four different methods of irradiating food.To determine which is best, it conducts an experiment where different foods are irradiated and the bacteria count is measured.As part of the experiment the following foods are irradiated: meat, poultry, veal, tuna, and yogurt.The results are shown below.
-{Food Irradiation Narrative} Can the company infer at the 1% significance level that differences in the bacteria count exist among the four irradiation methods?

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Q 123Q 123

Acid Reflux
A partial ANOVA table in a randomized block design is shown below, where the treatments refer to different acid reflux medicines, and the blocks refer to groups of men with similar levels of stomach acid.
-{Acid Reflux Narrative} Fill in the missing values (identified by asterisks) in the above ANOVA Table.

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Q 124Q 124

Acid Reflux
A partial ANOVA table in a randomized block design is shown below, where the treatments refer to different acid reflux medicines, and the blocks refer to groups of men with similar levels of stomach acid.
-{Acid Reflux Narrative} Can we infer at the 5% significance level that the treatment means differ?

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Q 125Q 125

Acid Reflux
A partial ANOVA table in a randomized block design is shown below, where the treatments refer to different acid reflux medicines, and the blocks refer to groups of men with similar levels of stomach acid.
-{Acid Reflux Narrative} Can we infer at the 5% significance level that the block means differ?

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Essay

Q 126Q 126

In a two-factor ANOVA, there are 4 levels for factor A and 5 levels for factor B, and two observations within each cell.The number of treatments in this experiment is 40.

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True False

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True False

Q 128Q 128

In a two-factor ANOVA, there are 5 levels for factor A, 4 levels for factor B, and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals 20.

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True False

Q 129Q 129

A complete factorial experiment is an experiment in which the number of replicates is the same for each treatment on which data is collected.

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True False

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True False

Q 131Q 131

In a two-factor ANOVA, the sum of squares due to both factors, the interaction sum of squares, and the error sum of squares must all add up to the total sum of squares.

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True False

Q 132Q 132

If there is enough evidence to conclude that there is interaction in a two-factor ANOVA, do not proceed to conduct the F-tests for each factor individually.

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True False

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True False

Q 134Q 134

In the two-factor ANOVA where a is the number of factor A levels, b is the number of factor B levels, and r is the number of replicates, the number of degrees of freedom for interaction is:
A) (a 1)(b 1)
B) abr 1
C) (a 1)(r 1)
D) n ab

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Multiple Choice

Q 135Q 135

When the effect of a level for one factor depends on which level of another factor is present, the most appropriate ANOVA design to use in this situation is the:
A) One-way ANOVA with 2 treatments.
B) Two-factor ANOVA with interaction.
C) Two-factor ANOVA with no interaction.
D) None of these choices.

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Multiple Choice

Q 136Q 136

In the two-factor ANOVA where a is the number of factor A levels, b is the number of factor B levels, r is the number of replicates, and n is the total number of observations, the number of degrees of freedom for error is:
A) (a 1)(b 1)
B) abr 1
C) r(a 1)(b 1)
D) n ab

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Multiple Choice

Q 137Q 137

In a two-factor ANOVA, there are 4 levels for factor A, 5 levels for factor B, and 3 observations for each combination of factor A and factor B levels.The number of treatments in this experiment equals:
A) 16
B) 20
C) 25
D) 60

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Multiple Choice

Q 138Q 138

In a two-factor ANOVA, there are 4 levels for factor A, 5 levels for factor B, and 3 observations for each combination of factor A and factor B levels.The total number of observations in this experiment equals:
A) 60
B) 25
C) 20
D) 16

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Multiple Choice

Q 139Q 139

In a two-factor ANOVA, where a is the number of factor A levels and b is the number of factor B levels, the number of degrees of freedom for the interaction term is
A) (a 1)(b 1)
B) ab 1
C) (a 1) + (b 1)
D) Unknown; need to know the number of replicates.

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Multiple Choice

Q 140Q 140

The equation: SS(Total) = SS(A) + SS(B) + SS(AB) + SSE applies to which ANOVA model?
A) One-way ANOVA with 2 treatments.
B) Two-factor ANOVA with interaction.
C) Two-factor ANOVA with no interaction.
D) None of these choices.

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Multiple Choice

Q 141Q 141

A complete 3 2 factorial experiment is called balanced if:
A) data is collected at all three levels of factor A.
B) data is collected at both levels of factor B.
C) the number of replicates is the same for each of the 6 treatments.
D) None of these choices.

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Multiple Choice

Q 142Q 142

Number of observation for particular combination of treatments is called a(n) ________________.

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Essay

Q 143Q 143

A(n) ____________________ experiment requires that the sample size for each treatment be equal.

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Q 145Q 145

In a(n) ____________________ factorial experiment, data for all possible combinations of the levels of the factors are gathered.

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Q 146Q 146

The required conditions for a two-factor ANOVA are that the distribution of the response is ____________________ distributed; the variance for each treatment is ____________________; and the samples are ____________________.

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Q 147Q 147

In a two-factor ANOVA, the total sum of squares is broken down into the sum of SS(A) + SS(B) + SSE + SS(____________________).

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Q 148Q 148

To test for interaction between factors A and B in a two-factor ANOVA, you use the F statistic that equals ____________________ divided by ____________________.

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Essay

Q 149Q 149

Migraine Treatments
The following data were generated from a 2 2 factorial experiment with 3 replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs, which physicians recommend to increase the effectiveness of the injections.Three migraine patients were randomly selected for each combination of injection and drug.
-{Migraine Treatments Narrative} Test at the 5% significance level to determine if differences exist among the four treatment means.

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Essay

Q 150Q 150

Migraine Treatments
The following data were generated from a 2 2 factorial experiment with 3 replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs, which physicians recommend to increase the effectiveness of the injections.Three migraine patients were randomly selected for each combination of injection and drug.
-{Migraine Treatments Narrative} Test at the 5% significance level to determine if differences exist among the levels of factor A.

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Essay

Q 151Q 151

Migraine Treatments
The following data were generated from a 2 2 factorial experiment with 3 replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs, which physicians recommend to increase the effectiveness of the injections.Three migraine patients were randomly selected for each combination of injection and drug.
-{Migraine Treatments Narrative} Test at the 5% significance level to determine if differences exist among the levels of factor B.

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Essay

Q 152Q 152

Keyboard Configuration and Size
The data shown below were taken from a 2 3 factorial experiment to examine the effects of factor A (keyboard configuration, 3 levels) and factor B (keyboard size, 2 levels) on typing speed.Each cell consists of the times needed for each of 4 randomly assigned keyboardists to type a standard document under each set of conditions (in minutes).
-{Keyboard Configuration and Size Narrative} Test at the 5% significance level to determine if time differences exist among the different keyboard configurations.

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Essay

Q 153Q 153

Keyboard Configuration and Size
The data shown below were taken from a 2 3 factorial experiment to examine the effects of factor A (keyboard configuration, 3 levels) and factor B (keyboard size, 2 levels) on typing speed.Each cell consists of the times needed for each of 4 randomly assigned keyboardists to type a standard document under each set of conditions (in minutes).
-{Keyboard Configuration and Size Narrative} Test at the 5% significance level to determine if time differences exist among the keyboard sizes.

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Essay