Deck 13: Analysis of Variance

Question 1

Which of the following is the correct interpretation of the Fisher's 100(1 - α)% confidence interval for μ_i - μ_j?

A) If the interval includes the value zero,the null hypothesis,that H₀: μ_i - μ_j = 0,is rejected for at α level of significance.
B) If the interval does not include the value zero,the null hypothesis,that H₀: μ_i - μ_j = 0,is rejected at 100(1 - α)% level of significance.
C) If the interval does not include the value zero,the null hypothesis,that H₀: μ_i - μ_j = 0,is rejected at α level of significance.
D) If the interval includes the value zero,the null hypothesis,that H₀: μ_i - μ_j = 0,is rejected at 100(1 - α)% level of significance.

Answer 1

C

Question 2

ANOVA is a statistical technique used to determine if differences exist between the means of two populations.

Answer 2

False

Question 3

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples.

Answer 3

True

Question 4

The variability due to chance,also known as within-treatments variability,is the estimate of σ² which is based on the _____________.

A) variability of the data across different samples
B) consistency of the data within each sample
C) variability of the data within each sample
D) reliability of the data within each sample

Question 5

When using Fisher's least difference (LSD)method at some stated significance level α,the probability of committing a Type I error increases as the number of pairwise comparisons increases.

Question 6

If the amount of variability between treatments is significantly greater than the amount of variability within treatments,then _________.

A) reject the null hypothesis of equal population means
B) do not reject the null hypothesis of equal population means
C) conclude that the ratio of between-treatments variability to within-treatments variability is significantly less than 1
D) perform further analysis using the two-way ANOVA with interaction

Question 7

The between-treatments variability is the estimate of σ2 which is based on the variability due to chance.

Question 8

If there are five treatments under study,the number of pairwise comparisons is _______.

A) 15
B) 5
C) 20
D) 10

Question 9

In general,blocks are the levels at which we hold an integral factor fixed,so that we can measure its contribution to the variation within the samples.

Question 10

When two factors interact,the effect of one factor on the population mean depends upon the specific value or level present for the other factor.

Question 11

Fisher's LSD method is applied when the _________________

A) ANOVA test has not rejected the null hypothesis of equal population means.
B) ANOVA test has rejected the null hypothesis of equal population means.
C) two-sample t test is not applicable.
D) None of these choices is correct.

Question 12

Which of the following is the Fisher's 100(1 - α)% confidence interval for the difference between two population means μ_i - μ_j?

A)
B)
C)
D)

Question 13

Which of the following is the assumption that is not applicable for a one-way ANOVA test?

A) The populations are normally distributed.
B) The population standard deviations are not all equal.
C) The samples are selected independently.
D) The sample is drawn at random from each population.

Question 14

One-way ANOVA analyzes the effect of one factor on the population mean.It is based on a _______.

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

Question 15

One-way ANOVA analyzes the effect of one factor on the population mean and it is based on a completely randomized design.

Question 16

The interaction test is performed before making any conclusions based on the tests for the main effects.

Question 17

If units within each block are randomly assigned to each of the treatments,then the design of the experiment is referred to as a completely randomized design.

Question 18

Between-treatments variability is based on a weighted sum of squared differences between the ____________________________________________________.

A) population variances and the overall mean of the data set
B) sample means and the overall mean of the data set
C) sample variances and the overall mean of the data set
D) population means and the overall mean of the data set

Question 19

When using Fisher's LSD method at some stated significance level,the probability of committing a Type I error increases as the number of _________________________.

A) pairwise comparisons decreases
B) pairwise comparisons increases
C) sample size increases
D) treatments decreases

Question 20

When the null hypothesis is rejected in an ANOVA test,Fisher's least significant difference method is superior to Tukey's honestly significant differences method to determine which population means differ.

Question 21

Which of the following formulas is used to compute the grand mean?

A)
B)
C)
D)

Question 22

If the interaction between two factors is not significant,the next tests to be done are ___________________.

A) none,the analysis is complete
B) none,gather more data
C) tests about the population means of factor A or factor B using two-way ANOVA without interaction
D) Tukey's confidence intervals

Question 23

Tukey's 100(1 −α)% confidence interval for the difference between two population means μ_i - μ_j for unbalanced data is given by ____________________.

A)
B)
C)
D)

Question 24

In a two-way ANOVA test,how many null hypotheses are tested?

A) 1
B) 1 or 2
C) 2 or 3
D) More than 3

Question 25

Tukey's HSD method uses _____ instead of _____ when compared to Fisher's LSD method for pairwise comparisons.

A) t values;studentized range values
B) studentized range values;F values
C) F values;t values
D) studentized range values;t values

Question 26

Which of the following is a correct formula for the test statistic for a one-way ANOVA test?

A)
B)
C)
D)

Question 27

If units with each block are randomly assigned to each of the treatments,then the design of the experiment is referred to as a _______________________.

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

Question 28

One of the disadvantages of Fisher's LSD method is that the probability of committing a _____________________________________________________________.

A) Type II error increases as the number of pairwise comparisons increases
B) Type I error increases as the number of pairwise comparisons decreases
C) Type II error increases as the number of pairwise comparisons decreases
D) Type I error increases as the number of pairwise comparisons increases

Question 29

Which of the following is a correct formula for the sum of squares due to treatments?

A) SSTR =
B) SSTR =
C) SSTR =
D) SSTR =

Question 30

Psychology students want to determine if there are differences between the ability of business majors and science majors to solve various types of analytic problems.They conduct an experiment and record the amount of time it takes to complete each analytic problem.The following two-way ANOVA table summarizes their findings. For the hypothesis test about the interaction term,the p-value is ______________.

A) less than 0.01
B) between 0.01 and 0.025
C) between 0.025 and 0.05
D) greater than 0.05

Question 31

Psychology students want to determine if there are differences between the ability of business majors and science majors to solve various types of analytic problems.They conduct an experiment and record the amount of time it takes to complete each analytic problem.The following Two-Way ANOVA table summarizes their findings. The number of different analytic problems the students solved is _____.

A) 1
B) 2
C) 4
D) 5

Question 32

Which of the following is a correct formula for the error sum of squares?

A) SSE =
B) SSE =
C) SSE =
D) SSE =

Question 33

Tukey's 100(1 - α)% confidence interval for the difference between two population means μ_i - μ_j for balanced data is given by ____________________.

A)
B)
C)
D)

Question 34

AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks,cars,and vans.The following data represent the age of a random sample of trucks,cars,and vans. The grand mean for these observations is ________.

A) 7.2
B) 8.0
C) 8.9
D) 9.3

Question 35

Tukey's honestly significant differences (HSD)method ensures that the probability of a Type I error remains fixed irrespective of the number of ________________.

A) pairwise comparisons
B) treatments
C) replications within each treatment
D) replications for each combination of factor A and factor B

Question 36

AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks,cars,and vans.The following data represent the age of a random sample of trucks,cars,and vans. The sum of squares within SSE for these observations is ________.

A) 22.4
B) 20.5
C) 41.8
D) 30.0

Question 37

AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks,cars,and vans.The following data represent the age of a random sample of trucks,cars,and vans. The mean square for treatments MSTR for these observations is ________.

A) 2.0
B) 4.7
C) 16.0
D) 12.5

Question 38

Psychology students want to determine if there are differences between the ability of business majors and science majors to solve various types of analytic problems.They conduct an experiment and record the amount of time it takes to complete each analytic problem.The following two-way ANOVA table summarizes their findings. At the 5% significance level,the conclusion for the hypothesis test about the interaction term is ______.

A) do not reject the null hypothesis;there is no evidence of an interaction effect between major and problem type
B) reject the null hypothesis;there is no evidence of an interaction effect between major and problem type
C) reject the null hypothesis;there is evidence of an interaction effect between major and problem type
D) do not reject the null hypothesis;there is evidence of an interaction effect between major and problem type

Question 39

Which of the following is the pooled estimate of the common population variance for Fisher's test?

A)
B)
C)
D)

Question 40

Psychology students want to determine if there are differences between the ability of business majors and science majors to solve various types of analytic problems.They conduct an experiment and record the amount of time it takes to complete each analytic problem.The following two-way ANOVA table summarizes their findings. At the 5% significance level,the critical value for the test about the interaction is less than ______.

A) 2.14
B) 2.69
C) 2.25
D) 2.51

Question 41

Which of the following is the correct degrees of freedom when computing MSE?

A) n_T - c - r + 1
B) n_T - 1
C) (c - 1)(r - 1)
D) cr(w - 1)

Question 42

Consider the partially completed two-way ANOVA (without interaction)summary table. The mean square for factor A is ______.

A) 200
B) 410
C) 160
D) 50

Question 43

Which of the following is the correct formula for the sum of squares SSA for factor A ?

A) SSA =
B) SSA =
C) SSA =
D) SSA =

Question 44

A career counselor wants to understand if the average annual earnings differ by educational attainment.The counselor uses three education levels: high school or less,undergraduate degree,and master's degree or more.After collecting data,the resulting incomplete one-way ANOVA table and Tukey's confidence intervals are shown below. a.Complete the ANOVA table.
b.Set up the competing hypothesis to test whether there are differences in mean annual salary between the different education levels.
c.At the 5% significance level,what is the conclusion to the test?
d.If significant differences exist,use Tukey's confidence intervals to determine which educational levels have different mean annual earnings.

Question 45

Consider the partially completed two-way ANOVA (with interaction)summary table. The mean square error (MSE)is _____.

A) 21
B) 43
C) 32
D) 26

Question 46

A farmer plants tomato seeds into four different plots.In each plot,there is a different fertilizer treatment that is applied to the soil.After three weeks,he measures the height of each tomato plant from each of the four plots.The data he collects is given below. a.Construct an ANOVA table.
b.Set up the competing hypothesis to test whether there are some differences in the mean heights between the different plots/fertilizers.
c.At the 5% significance level,what is the conclusion to the test?
d.Consider the sample standard deviations for each plot.Which of the assumptions might be violated?

Question 47

Consider the partially completed two-way ANOVA (without interaction)summary table. Which of the following is the value of the test statistic for factor B?

A) 3.20
B) 6.70
C) 5.16
D) 4.00

Question 48

A career counselor wants to understand if the average salary differs by educational attainment blocking on industry.The counselor uses four degree levels (high school,undergraduate,master's,and doctoral)and three industries.The study resulted in the following incomplete ANOVA table. a.Complete the ANOVA table.
b.At the 5% significance level,can you conclude the average salary differs by educational attainment?
c.At the 5% significance level,can you conclude the average salary differs by industry?

Question 49

A regional sales manager of a bank wants to know if the number of ATM transactions per day is different for four cities of equal size in the executive's region.The executive collects relevant data and obtains the following incomplete One-Way ANOVA table. a.Complete the ANOVA table.
b.Set up the competing hypothesis to test whether there are differences in the mean number of ATM transactions per day between the different cities.
c.At the 5% significance level,what is the conclusion to the test?

Question 50

A career counselor wants to determine if there is an interaction between gender (male or female)and sector (private or public)on average weekly income.The counselor obtains data and produces the following incomplete two-way ANOVA table. a.Complete the ANOVA table.
b.At the 5% significance level,can you conclude there is interaction between gender and sector?
c.Are you able to conduct tests on the main effects? If yes,conduct these tests at the 5% significance level.
d.Why is a two-way ANOVA (with or without interaction)preferable to two two-sample T-tests in this situation?

Question 51

A fund manager suspects there is an interaction between fund market cap (either small,mid,or large)and the fund objective (either growth or value)on the average annual fund performance.The fund manager obtains data and produces the following incomplete two-way ANOVA table. a.Complete the ANOVA table.
b.At the 5% significance level,can you conclude there is interaction between market cap and objective?
c.Are you able to conduct tests on the main effects? If yes,conduct these tests at the 5% significance level.

Question 52

Consider the partially completed two-way ANOVA (with interaction)summary table. The degrees of freedom for the interaction of factors A and B is _____.

A) 6
B) 4
C) 3
D) 5

Question 53

Consider the partially completed two-way ANOVA (without interaction)summary table. The sum of squares for factor A is ______.

A) 930
B) 800
C) 1,150
D) 980

Question 54

A research firm wants to compare the miles per gallon (mpg)for three different types of gasoline.To control for the performance of different types of cars,seven types of cars were used as the blocks.The study yielded the below as the following incomplete two-way ANOVA table. a.Complete the ANOVA table.
b.At the 5% significance level,can you conclude if the average mpg differs by gas type?
c.At the 5% significance level,can you conclude if the average mpg differs by car type?

Question 55

Consider the partially completed two-way ANOVA (with interaction)summary table. The mean square for interaction MSAB is _____.

A) 50
B) 24
C) 75
D) 65

Question 56

Which of the following is the correct formula for the error sum of squares SSE?

A) SSE = SST - (SSA + SSB + SSAB)
B) SSE = SST - (SSA - SSB)
C) SSE = SST + SSA + SSB
D) SSE = SST - (SSA + SSB)

Question 57

A farmer plants tomato seeds into four different plots.In each plot,there is a different fertilizer treatment that is applied to the soil.After conducting the hypothesis test for the mean heights,he obtains Tukey's confidence intervals which are below. Use Tukey's confidence intervals to determine which plots/fertilizers have different mean heights.

Question 58

Consider the partially completed two-way ANOVA (with interaction)summary table. The interaction test statistic is ____.

A) 3.16
B) 4.80
C) 2.56
D) 0.75