Question 1

Fill in the blanks (identified by asterisks) in the following partial ANOVA table. $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Source of Variation } & \text { SS } & d f & M S & F \
\hline \text { Treatments } & * & * & 79.95 & * \
\hline \text { Error } & 17.0 & * & * & \
\hline \text { Total } & 176.9 & 10 & & \
\hline
\end{array}$$

Accepted Answer

The answer of Fill in the blanks (identified by asterisks)...

Question 2

Automobile insurance appraisers examine cars 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 cars that have recently been damaged in accidents. Three appraisers then estimate the repair costs of all six cars. From the data shown below, can we infer at the 5% significance level that the executive's claim is true? $$\begin{array} { | c | c | c | c | } 
\hline & &{ \text { Estimated repair cost } } \
\hline \text { Car } & \text { Appraiser 1 } & \begin{array} { c } 
\text { Appraiser } \
2
\end{array} & \text { Appraiser 3 } \
\hline 1 & 650 & 600 & 750 \
\hline 2 & 930 & 910 & 1010 \
\hline 3 & 440 & 450 & 500 \
\hline 4 & 750 & 710 & 810 \
\hline 5 & 1190 & 1050 & 1250 \
\hline 6 & 1560 & 1270 & 1450 \
\hline
\end{array}$$

Accepted Answer

\[\begin{array} { | l | c | c | c | c |

Question 3

A randomised 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.

Accepted Answer

A) True 
 B)False

Question 4

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: $\begin{array}{|l|l|}
\hline  A.&\text { all popul ation means are equal}\
\hline  B.&\text {all population means differ. }\
\hline  C.&\text { at least two population means are equal.}\
\hline  D.&\text {at least two population means differ. }\
\hline 
\end{array}$

Accepted Answer

The answer of One-way ANOVA is applied to independent samples...

Question 5

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 variation within the samples.

Accepted Answer

A) True 
 B)False

Question 6

In one-way analysis of variance, within-treatments variation stands for the: $\begin{array}{|l|l|}
\hline  A.&\text { sum of squares for error.}\
\hline  B.&\text {sum of squares for treatments. }\
\hline  C.&\text { total sum of squares.}\
\hline  D.&\text {None of these choices are correct. }\
\hline 
\end{array}$

Accepted Answer

The answer of In one-way analysis of variance, within-treatments variation...

Question 7

Statistics practitioners use the analysis of variance (ANOVA) technique to compare two or more populations of interval data.

Accepted Answer

A) True 
 B)False

Question 8

The strength of a weld depends to some extent on the metal alloy used in the welding process. A scientist working in the research laboratory of a major automobile manufacturer has developed three new alloys. In order to test their strengths, each alloy is used in several welds. The strengths of the welds are then measured, with the results shown below. Can the scientist conclude at the 5% significance level that differences exist among the strengths of the welds with the different alloys? $$\begin{array} { | c | c | c | } 
\hline & { \text { Strenghh of welds } } \
\hline \text { Alloy 1 } & \text { Alloy } 2 & \text { Alloy } 3 \
\hline 15 & 17 & 25 \
\hline 23 & 21 & 27 \
\hline 16 & 19 & 24 \
\hline 29 & 25 & 31 \
\hline & 28 & 23 \
\hline & 19 & \
\hline
\end{array}$$

Accepted Answer

@#IMG-DLM& @#IMG-DLM& . @#IMG-DLM& At least two me

Question 9

In one-way ANOVA, suppose that there are five treatments with $$n _ { 1 } = n _ { 2 } = n _ { 3 } = 5$$ and $$n _ { 4 } = n _ { 5 } = 7$$ . Then the mean square for error, MSE, equals: $\begin{array}{|l|l|}
\hline \text { A. } & \mathrm{SSE} / 4 . \
\hline \text { B. } & \mathrm{SSE} / 29 . \
\hline \text { C. } & \mathrm{SSE} / 24 \
\hline \text { D. } & \mathrm{SSE} / 5 . \
\hline
\end{array}$

Accepted Answer

The answer of In one-way ANOVA, suppose that there are...

Question 10

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: $\begin{array}{|l|l|}
\hline  A.&\text {one-way ANOVA. }\
\hline  B.&\text { two-way ANOVA.}\
\hline  C.&\text {randomised block design. }\
\hline  D.&\text {matched pairs design. }\
\hline 
\end{array}$

Accepted Answer

The answer of When the effect of a level for...

Question 11

Consider the following partial ANOVA table: $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Source of Variation } & \text { SS } & d f & M S & F \
\hline \text { Treatments } & 75 & * & 25 & 6.67 \
\hline \text { Error } & 60 & * & 3.75 & \
\hline \text { Total } & 135 & 19 & & \
\hline
\end{array}$$ The numbers of degrees of freedom for numerator and denominator, respectively, (identified by asterisks) are: $\begin{array}{|l|l|}
\hline\text { A. } & 4 \text { and } 15 . \
\hline \text { B. } & 3 \text { and } 16 . \
\hline \text { C. } & 15 \text { and } 4 . \
\hline \text { D. } & 16 \text { and } 3 . \
\hline
\end{array}$

Accepted Answer

The answer of Consider the following partial ANOVA table: \[\begin{array}...

Question 12

Three tennis players, one a beginner, one experienced and one a professional, have been randomly selected from the membership of a large city tennis club. Using the same ball, each person hits four serves with each of five racquet models, with the five racquet models selected randomly. Each serve is clocked with a radar gun and the result recorded. Among ANOVA models, this setup is most like the single-factor analysis of variance: independent samples.

Accepted Answer

A) True 
 B)False

Question 13

In the randomised block design ANOVA, the sum of squares for error equals: $\begin{array}{|l|l|}
\hline\text { A. } & \text { SS(Total) - SST. } \
\hline \text { B. } & \text { SS(Total) - SSB } \
\hline \text { C. } & \text { SS(Total) - SST - SSB. } \
\hline \text { D. } & \text { SS(Total) - SS(A) - SS(B) - SS(AB) } \
\hline
\end{array}$

Accepted Answer

The answer of In the randomised block design ANOVA, the...

Question 14

In one-way ANOVA, the term $\overline { \bar { x } }$ refers to the: $\begin{array}{|l|l|}
\hline  A.&\text { sum of the sample means.}\
\hline  B.&\text {sum of the sample means divided by the total number of observations. }\
\hline  C.&\text { sum of the population means.}\
\hline  D.&\text {weighted mean of the sample means. }\
\hline 
\end{array}$

Accepted Answer

The answer of In one-way ANOVA, the term \(\overline {...

Question 15

Which of the following is a required condition for one-way ANOVA? A. The populations must all be normally distributed.
B. The population variances must be equal.
C. The samples for each treatment must be selected randomly and independently.
D. All of these choices are correct.

Accepted Answer

The answer of Which of the following is a required...

Question 16

When the data are obtained through a controlled experiment in the single-factor ANOVA, we call the experimental design the completely randomised design of the analysis of variance.

Accepted Answer

A) True 
 B)False

Question 17

Given the significance level 0.025, the F-value for the numbers of degrees of freedom d.f. = (4, 8) is 5.05.

Accepted Answer

A) True 
 B)False

Question 18

A federal politician wants to investigate the difference in average weekly losses of workers due to accidents between South Australia (SA) and Western Australia (WA). The following table shows the average weekly losses of worker hours due to accidents in 2012 at five randomly selected manufacturing firms in each of SA and WA. $$\begin{array} { | c | c | } 
\hline \text { SA } & \text { WA } \
\hline 35 & 39 \
\hline 73 & 83 \
\hline 55 & 34 \
\hline 125 & 98 \
\hline 33 & 42 \
\hline
\end{array}$$ Assume that the weekly losses of worker hours are normally distributed.
Is there a significant difference between the average weekly losses of workers hours due to accidents between SA and WA?
Test at the 5% significance level.
(Hint: Perform an F-test for one-way ANOVA to determine whether the population means differ.)

Accepted Answer

Ho: µ₁= µ₂ H_A: µ₁≠ µ₂ @#IMG-DLM& Rejection region: F >

Question 19

The F-test of the analysis of variance requires that the populations be normally distributed with equal variances.

Accepted Answer

A) True 
 B)False

Question 20

If we want to conduct a test to determine whether a population mean is greater than another population mean, we: $\begin{array}{|l|l|}
\hline \text { A. } & \text { can use the analysis of variance. } \
\hline \text { B. } & \text { must use the independent-samples } t \text {-test for the difference between two means. } \
\hline \text { C. } & \text { must use the chi-squared test. } \
\hline \text { D. } & \begin{array}{l}
\text { can use the analysis of variance or can use the independent-samples } t \text {-test for the } \
\text { difference between two means. }
\end{array} \
\hline
\end{array}$

Accepted Answer

The answer of If we want to conduct a test...

Fill in the blanks (identified by asterisks) in the following partial ANOVA table. Source of Variation SS df MS F Treatments * * 79.95 * Error 17.0 * * Total 176.9 10

A randomised 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.

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 variation within the samples.

In one-way analysis of variance, within-treatments variation stands for the: A. sum of squares for error. B. sum of squares for treatments. C. total sum of squares. D. None of these choices are correct.

Statistics practitioners use the analysis of variance (ANOVA) technique to compare two or more populations of interval data.

In one-way ANOVA, suppose that there are five treatments with $n _ { 1 } = n _ { 2 } = n _ { 3 } = 5$ and $n _ { 4 } = n _ { 5 } = 7$ . Then the mean square for error, MSE, equals: A. /4. B. /29. C. /24 D. /5.

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. B. two-way ANOVA. C. randomised block design. D. matched pairs design.

Consider the following partial ANOVA table: Source of Variation SS df MS F Treatments 75 * 25 6.67 Error 60 * 3.75 Total 135 19 The numbers of degrees of freedom for numerator and denominator, respectively, (identified by asterisks) are: A. 4 and 15. B. 3 and 16. C. 15 and 4. D. 16 and 3.

In the randomised block design ANOVA, the sum of squares for error equals: A. SS(Total) - SST. B. SS(Total) - SSB C. SS(Total) - SST - SSB. D. SS(Total) - SS(A) - SS(B) - SS(AB)

In one-way ANOVA, the term $\overline { \bar { x } }$ refers to the: A. sum of the sample means. B. sum of the sample means divided by the total number of observations. C. sum of the population means. D. weighted mean of the sample means.

Which of the following is a required condition for one-way ANOVA? A. The populations must all be normally distributed. B. The population variances must be equal. C. The samples for each treatment must be selected randomly and independently. D. All of these choices are correct.

When the data are obtained through a controlled experiment in the single-factor ANOVA, we call the experimental design the completely randomised design of the analysis of variance.

Given the significance level 0.025, the F-value for the numbers of degrees of freedom d.f. = (4, 8) is 5.05.

The F-test of the analysis of variance requires that the populations be normally distributed with equal variances.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 16: Analysis of Variance

Fill in the blanks (identified by asterisks) in the following partial ANOVA table. Source of Variation SS df MS F Treatments * * 79.95 * Error 17.0 * * Total 176.9 10

A randomised 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.

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 variation within the samples.

In one-way analysis of variance, within-treatments variation stands for the: A. sum of squares for error. B. sum of squares for treatments. C. total sum of squares. D. None of these choices are correct.

Statistics practitioners use the analysis of variance (ANOVA) technique to compare two or more populations of interval data.

In one-way ANOVA, suppose that there are five treatments with n1=n2=n3=5n _ { 1 } = n _ { 2 } = n _ { 3 } = 5n1​=n2​=n3​=5 and n4=n5=7n _ { 4 } = n _ { 5 } = 7n4​=n5​=7 . Then the mean square for error, MSE, equals: A. /4. B. /29. C. /24 D. /5.

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. B. two-way ANOVA. C. randomised block design. D. matched pairs design.

Consider the following partial ANOVA table: Source of Variation SS df MS F Treatments 75 * 25 6.67 Error 60 * 3.75 Total 135 19 The numbers of degrees of freedom for numerator and denominator, respectively, (identified by asterisks) are: A. 4 and 15. B. 3 and 16. C. 15 and 4. D. 16 and 3.

In the randomised block design ANOVA, the sum of squares for error equals: A. SS(Total) - SST. B. SS(Total) - SSB C. SS(Total) - SST - SSB. D. SS(Total) - SS(A) - SS(B) - SS(AB)

In one-way ANOVA, the term xˉ‾\overline { \bar { x } }xˉ refers to the: A. sum of the sample means. B. sum of the sample means divided by the total number of observations. C. sum of the population means. D. weighted mean of the sample means.

Which of the following is a required condition for one-way ANOVA? A. The populations must all be normally distributed. B. The population variances must be equal. C. The samples for each treatment must be selected randomly and independently. D. All of these choices are correct.

When the data are obtained through a controlled experiment in the single-factor ANOVA, we call the experimental design the completely randomised design of the analysis of variance.

Given the significance level 0.025, the F-value for the numbers of degrees of freedom d.f. = (4, 8) is 5.05.

The F-test of the analysis of variance requires that the populations be normally distributed with equal variances.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

In one-way ANOVA, suppose that there are five treatments with $n _ { 1 } = n _ { 2 } = n _ { 3 } = 5$ and $n _ { 4 } = n _ { 5 } = 7$ . Then the mean square for error, MSE, equals: A. /4. B. /29. C. /24 D. /5.

In one-way ANOVA, the term $\overline { \bar { x } }$ refers to the: A. sum of the sample means. B. sum of the sample means divided by the total number of observations. C. sum of the population means. D. weighted mean of the sample means.