Deck 11: Statistical Inferences for Population Variances

Question 1

In one-way ANOVA,the numerator degrees of freedom equals the number of samples being compared.

Answer 1

False

Question 2

In one-way ANOVA,a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

Answer 2

False

Question 3

When using a randomized block design,the interaction effect between the block and treatment factors cannot be separated from the error term.

Answer 3

True

Question 4

The experimentwise α for the 95 percent individual confidence interval for μ₁ − μ₂ (treatment mean 1 − treatment mean 2)will always be smaller than the experimentwise α for a Tukey 95 percent simultaneous confidence interval for μ₁ − μ₂.

Question 5

If factors being studied cannot be controlled,the data are said to be observational.

Question 6

Interaction exists between two factors if the relationship between the mean response and one factor depends on the other factor.

Question 7

In a completely randomized (one-way)ANOVA,with other things being equal,as the sample means get closer to each other,the probability of rejecting the null hypothesis decreases.

Question 8

The error sum of squares measures the between-treatment variability.

Question 9

In one-way ANOVA,the numerator of the F statistic is an estimate of the population variance based on within-treatment variation.

Question 10

The ANOVA procedure for a two-factor factorial experiment partitions the total sum of squares into three components,SS first factor,SS second factor,and SSE.

Question 11

The 95 percent individual confidence interval for μ₁ − μ₂ (treatment mean 1 − treatment mean 2)will always be smaller than the Tukey 95 percent simultaneous confidence interval for μ₁ − μ₂.

Question 12

After rejecting the null hypothesis of equal treatments,a researcher decided to compute a 95 percent confidence interval for the difference between the mean of treatment 1 and mean of treatment 2 based on the Tukey procedure.At α = .05,if the confidence interval includes the value of zero,then we can reject the hypothesis that the two population means are equal.

Question 13

Experimental data are collected so that the values of the dependent variables are set before the values of the independent variable are observed.

Question 14

In one-way ANOVA,other factors being equal,the further apart the treatment means are from each other,the more likely we are to reject the null hypothesis associated with the ANOVA F test.

Question 15

In a 2-way ANOVA,treatment is considered to be a combination of a level of factor 1 and a level of factor 2.

Question 16

Different levels of a factor are called ____________.

A) treatments
B) variables
C) responses
D) observations

Question 17

In a 2-way ANOVA,if factor 1 has a levels and factor 2 has b levels,then there are a total of _______ treatments.

A) a + b
B) a × b
C) |a − b|
D) a/b
E) a

Question 18

If sample mean plots look essentially parallel,we can intuitively conclude that there is an interaction between the two factors.

Question 19

A one-way analysis of variance is a method that allows us to estimate and compare the effects of several treatments on a response variable.

Question 20

In one-way ANOVA,as the between-treatment variation decreases,the probability of rejecting the null hypothesis increases.

Question 21

We have just performed a one-way ANOVA on a given set of data and did not reject the null hypothesis for the ANOVA F test.Assume that we are able to perform a randomized block design ANOVA on the same data.For the randomized block design ANOVA,the null hypothesis for equal treatments will ___________ be rejected.

A) always
B) sometimes
C) never

Question 22

Which of the following is not an assumption for one-way analysis of variance?

A) The p populations of values of the response variable associated with the treatments have equal variances.
B) The samples of experimental units associated with the treatments are randomly selected.
C) The experimental units associated with the treatments are independent samples.
D) The number of sampled observations must be equal for all p treatments.
E) The distribution of the response variable is normal for all treatments.

Question 23

When using a completely randomized design (one-way analysis of variance),the calculated F statistic will decrease as

A) the variability among the groups decreases relative to the variability within the groups.
B) the total variability increases.
C) the total variability decreases.
D) the variability among the groups increases relative to the variability within the groups.

Question 24

We have just performed a one-way ANOVA on a given set of data and rejected the null hypothesis for the ANOVA F test.Assume that we are able to perform a randomized block design ANOVA on the same data.For the randomized block design ANOVA,the null hypothesis for equal treatments will __________ be rejected.

A) always
B) sometimes
C) never

Question 25

When computing individual confidence intervals using the t statistic,for all possible pairwise comparisons of means,the experimentwise error rate will be

A) equal to α..
B) less than α.
C) greater than α.

Question 26

In the randomized block ANOVA,the sum of squares for factor 1 equals

A) SSTO − SS(error)− SS(interaction).
B) SSTO − SS(factor 2)− SSE.
C) SSTO − SS(interaction)− SS(factor 2).
D) SSTO − SS(factor 2).
E) SSTO − SS(error).

Question 27

When computing a confidence interval for the difference between two means,the width of the (1 − α)confidence interval based on the Tukey procedure will be __________ the width of the (1 − α)individual confidence interval based on the t statistic.

A) greater than
B) less than
C) the same as
D) sometimes greater than,sometimes less than

Question 28

ANOVA table The Excel/MegaStat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners.The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt.At a significance level of .05,the null hypothesis for the ANOVA F test is rejected.Analysis of the Tukey simultaneous confidence intervals shows that at the significance level (experimentwise)of .05,we would conclude that

A) all four brands of vacuum cleaners differ from each other in terms of their performance.
B) brand 1 differs from brand 2,and brand 2 differs from brand 3,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
C) brand 1 differs from brand 2,and brand 3 differs from brands 1,2,and 4,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
D) only brand 3 differs from the other three brands (brands 1,2,and 3),while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.
E) none of the four brands of vacuum cleaners differ from each other in terms of their performance.

Question 29

In a completely randomized ANOVA,with other things equal,as the sample means get closer to each other,the probability of rejecting the null hypothesis

A) decreases.
B) increases.
C) is unaffected.

Question 30

The advantage of the randomized block design over the completely randomized design is that we are comparing the treatments by using ________ experimental units.

A) randomly selected
B) the same
C) different
D) representative
E) equally timed

Question 31

A sum of squares that measures the variability among the sample means is referred to as the

A) treatment sum of squares.
B) error sum of squares.
C) sum of squares within-treatment.
D) total sum of squares.
E) interaction sum of squares.

Question 32

In a completely randomized (one-way)analysis of variance problem with c groups and a total of n observations in all groups,the variance between groups is equal to

A) (Total sum of squares)− (Sum of squares within columns).
B) (Sum of squares between columns)/(c − 1).
C) (Total sum of squares)− [(Sum of squares within columns)/(n − c)].
D) [(Total sum of squares)/(n − 1)] − [(Sum of squares between columns)/(c − 1)].

Question 33

ANOVA table The Excel/MegaStat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners.The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt.At a significance level of .05,we would

A) not be able to reject the null hypothesis of equal population means.
B) reject the null hypothesis of equal population means.
C) reject or fail to reject depending on the value of the t statistic.
D) not be able to decide whether or not to reject the null hypothesis due to insufficient information.

Question 34

A sum of squares that measures the total amount of variability in the observed values of the response variable is referred to as the

A) treatment sum of squares.
B) error sum of squares.
C) sum of squares within-treatment.
D) total sum of squares.
E) interaction sum of squares.

Question 35

In the one-way ANOVA,the treatment sum of squares equals

A) SSTO − SS(error)− SS(interaction).
B) SSTO − SS(factor 1)− SSE.
C) SSTO − SS(interaction)− SS(factor 1)− SS(factor 2).
D) SSTO − SS(factor 1)− SS(factor 2).
E) SSTO − SS(error).

Question 36

Which one of the following is not an assumption of one-way analysis of variance?

A) random selection of samples from each population
B) equality of the population variances
C) equality of the population means
D) Samples selected from each treatment population all have normal distributions.

Question 37

When we compute 100(1 − α)confidence intervals,the value of α is called the

A) comparisonwise error rate.
B) Tukey simultaneous error rate.
C) experimentwise error rate.
D) pairwise error rate.

Question 38

___________ simultaneous confidence intervals test all of the pairwise differences between means,respectively,while controlling the overall Type I error.

A) Randomized
B) Tukey
C) Covariate
D) Interacting

Question 39

After analyzing a data set using the one-way ANOVA model,the same data are analyzed using the randomized block design ANOVA model.SS (Treatment)in the one-way ANOVA model is _______________ the SS (Treatment)in the randomized block design ANOVA model.

A) always equal to
B) always greater than
C) always less than
D) sometimes greater than

Question 40

When computing confidence intervals using the Tukey procedure,for all possible pairwise comparisons of means,the experimentwise error rate will be

A) equal to α.
B) less than α.
C) greater than α.

Question 41

In a one-way analysis of variance with three treatments,each with five measurements,in which a completely randomized design is used,what is the degrees of freedom for treatments?

Question 42

In one-way ANOVA,the total sum of squares is equal to _______________________.

A) Treatment SS + Error SS
B) Treatment SS − Error SS
C) Treatment SS × Error SS
D) Treatment SS/Error SS

Question 43

In a one way ANOVA table,the ___________ the value of MSE,the higher the probability of rejecting the hypothesis that all treatment means are equal.

A) closer to 1
B) closer to 0
C) larger
D) smaller

Question 44

___________ refers to applying a treatment to more than one experimental unit.

A) Randomization
B) Balanced experiment
C) One-way ANOVA
D) Replication

Question 45

The dependent variable,the variable of interest in an experiment,is also called the ___________ variable.

A) categorical
B) regression
C) response
D) factor

Question 46

In performing a one-way ANOVA,_________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response and its corresponding treatment mean.

A) SS Error
B) SS Treatment
C) SS Total
D) SS Treatment/SS Error

Question 47

In general,a Tukey simultaneous 100(1 − α)percent confidence interval is _________ the corresponding individual 100(1 − α)percent confidence interval.

A) wider than
B) narrower than
C) no different from
D) two times more than

Question 48

The ___________________ units are the entities (objects,people,etc. )to which the treatments are assigned.

A) variable
B) block
C) experimental
D) random

Question 49

A ___________ design is an experimental design that compares v treatments by using d blocks,where each block is used exactly once to measure the effect of each treatment.

A) one-way ANOVA
B) two-way ANOVA
C) randomized block
D) balanced complete factorial

Question 50

In performing a one-way ANOVA,the _________ is the between-group variance.

A) MS Error
B) MS Treatment
C) SS Error
D) SS Treatment

Question 51

The F test for testing the difference between means is equal to the ratio of Mean Square _____________ over Mean Square __________________.

A) Treatment,Error
B) Error,Treatment
C) Treatment,Total
D) Error,Total

Question 52

In a ___________________ experimental design,independent random samples of experimental units are assigned to the treatments.

A) one-way ANOVA
B) two-way ANOVA
C) randomized block
D) balanced complete factorial

Question 53

The variable of interest in an experiment is referred to as the __________ variable.

A) categorical
B) regression
C) response
D) factor

Question 54

If the total sum of squares in a one-way analysis of variance is 25 and the treatment sum of squares is 17,then what is the error sum of squares?