The following equation applies to which ANOVA model? SS(Total) = SST + SSE. $\begin{array}{|l|l|} \hline \text { A. } & \text { One-way ANOVA } \\ \hline \text { B. } & \text { Two-way ANOVA. } \\ \hline \text { C. } & \text { Completely randomised design. } \\ \hline \text { D. } & \text { Randomised block design. } \\ \hline \end{array}$

The answer of The following equation applies to which ANOVA...

A partial ANOVA table in a randomised block design is shown below. \[\begin{array} { | l | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & d f & M S & F \\ \hline \text { Treatments } & * & 3 & * & * \\ \hline \text { Blocks } & 1256 & 2 & * & * \\ \hline \text { Error } & * & * & 67.67 & \\ \hline \text { Total } & 2922 & 11 & & \\ \hline \end{array}\] Can we infer at the 5% significance level that the block means differ?

H 0 : @#LAT-DLM& 1 = @#LAT-DLM& 2 = @#LAT-DLM& 3 H 1 :At least two mean

A partial ANOVA table in a randomised block design is shown below. \[\begin{array} { | l | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & d f & M S & F \\ \hline \text { Treatments } & * & 3 & * & * \\ \hline \text { Blocks } & 1256 & 2 & * & * \\ \hline \text { Error } & * & * & 67.67 & \\ \hline \text { Total } & 2922 & 11 & & \\ \hline \end{array}\] Can we infer at the 5% significance level that the treatment means differ?

H 0 : @#LAT-DLM& 1 = @#LAT-DLM& 2 = @#LAT-DLM& 3 = @#LAT-DLM& 4 H 1 :At least two m

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 likely false if: $\begin{array}{|l|l|} \hline \text { A. } & \text { MST is much larger than MSE. } \\ \hline \text { B. } & \text { MST is much smaller than MSE. } \\ \hline \text { C. } & \text { MST is equal to MSE. } \\ \hline \text { D. } & \text { MST is zero. } \\ \hline \end{array}$

The answer of In a single-factor analysis of variance, MST...

In a completely randomised design, 7 experimental units were assigned to the first treatment, 13 units to the second treatment, and 10 units to the third treatment. A partial ANOVA table for this experiment is shown below. \[\begin{array} { | l | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & d f & M S & F \\ \hline \text { Treatments } & * & * & * & 1.50 \\ \hline \text { Error } & * & * & 4 & \\ \hline \text { Total } & * & * & & \\ \hline \end{array}\] Fill in the blanks (identified by asterisks) in the above ANOVA table.

The answer of In a completely randomised design, 7 experimental...

In a completely randomised 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. \[\begin{array} { | l | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & d f & M S & F \\ \hline \text { Treatments } & * & * & 240 & * \\ \hline \text { Error } & * & * & * & \\ \hline \text { Total } & 2512 & * & & \\ \hline \end{array}\]

The answer of In a completely randomised design, 15 experimental...

Which of the following best describes an experimental design model where the treatments are defined as the levels of one factor, and the experimental design specifies independent samples? $\begin{array}{|l|l|} \hline \text { A. } & \text { Randomised block design } \\ \hline \text { B. } & \text { Two way ANOVA } \\ \hline \text { C. } & \text { One way ANOVA } \\ \hline \text { D. } & \text { All of these choices are correct. } \\ \hline \end{array}$

The answer of Which of the following best describes an...

Exam 16: Analysis of Variance

One-way ANOVA is applied to three independent samples having means 12, 15 and 20, respectively. If each observation in the third sample were increased by 40, the value of the F-statistic would increase by 40.

(True/False)

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Question 81

In an ANOVA test, the test statistic is F = 3.08. The rejection region is F > 3.07 for the 5% level of significance, F > 3.82 for the 2.5% level, and F > 4.87 for the 1% level. For this test, the p-value is: A. greater than 0.05 . B. between 0.01 and 0.025 . C. between 0.025 and 0.05 . D. smaller than 0.01 .

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Question 82

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

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Question 83

One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances. The following summary statistics are calculated: $n _ { 1 } =$ 18, $\bar { x } _ { 1 } =$ 15, $s _ { 1 } =$ 2. $n _ { 2 } =$ 10, $\bar { x } _ { 2 } =$ 20, $s _ { 2 } =$ 3. $n _ { 3 } =$ 12, $\bar { x } _ { 3 } =$ 16, $s _ { 3 } =$ 1. The within-treatments variation equals: A. 82.95. B. 160. C. 19.2. D. 165.9

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Question 84

In ANOVA, a factor is an independent variable.

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Question 85

The following equation applies to which ANOVA model? SS(Total) = SST + SSE. A. One-way ANOVA B. Two-way ANOVA. C. Completely randomised design. D. Randomised block design.

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Question 86

Provide an example of a randomised block design with three treatments (k = 3) and four blocks (b = 4), in which SSB = 0 and SST and SSE are not equal to zero.

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Question 87

Which of the following is true of the F-distribution? A. It is skewed to the right. B. Its values are always positive. C. It is used in the ANOVA test. D. All of these choices are correct

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Question 88

In a completely randomised design for ANOVA, the numbers of degrees of freedom for the numerator and denominator are 3 and 25, respectively. The total number of observations must equal: A. 28. B. 25. C. 22. D. 29.

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Question 89

One-way ANOVA is performed on independent samples taken from three normally distributed populations with equal variances. The following summary statistics were calculated: $n _ { 1 } =$ 7, $\bar { x } _ { 1 } =$ 65, $s _ { 1 } =$ 4.2. $n _ { 2 } =$ 8, $\bar { x } _ { 2 } =$ 59, $s _ { 2 } =$ 4.9. $n _ { 3 } =$ 9, $\bar { x } _ { 3 } =$ 63, $s _ { 3 } =$ 4.6. The value of the test statistics, F, equals: A. 71.250 B. 0.322. C. 21.104 D. 3.376.

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Question 90

A partial ANOVA table in a randomised block design is shown below. Source of Variation SS df MS F Treatments * 3 * * Blocks 1256 2 * * Error * * 67.67 Total 2922 11 Can we infer at the 5% significance level that the block means differ?

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Question 91

The number of degrees of freedom for the denominator of a one-way ANOVA test for 5 population means with 12 observations sampled from each population is 55.

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Question 92

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 treatments is given by: A. $k-1$ . B. $n-k$ . C. $n-1$ . D. $n-k+1$ .

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Question 93

A partial ANOVA table in a randomised block design is shown below. Source of Variation SS df MS F Treatments * 3 * * Blocks 1256 2 * * Error * * 67.67 Total 2922 11 Can we infer at the 5% significance level that the treatment means differ?

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Question 94

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 likely false if: A. MST is much larger than MSE. B. MST is much smaller than MSE. C. MST is equal to MSE. D. MST is zero.

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Question 95

Given the significance level 0.05, the F-value for the numbers of degrees of freedom d.f. = (9, 6) is 4.10.

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Question 96

In a completely randomised design, 7 experimental units were assigned to the first treatment, 13 units to the second treatment, and 10 units to the third treatment. A partial ANOVA table for this experiment is shown below. Source of Variation SS df MS F Treatments * * * 1.50 Error * * 4 Total * * Fill in the blanks (identified by asterisks) in the above ANOVA table.

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Question 97

In a completely randomised 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. Source of Variation SS df MS F Treatments * * 240 * Error * * * Total 2512 *

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Question 98

Which of the following best describes an experimental design model where the treatments are defined as the levels of one factor, and the experimental design specifies independent samples? A. Randomised block design B. Two way ANOVA C. One way ANOVA D. All of these choices are correct.

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Question 99

A study is to be undertaken to examine the effects of two kinds of background music and of two assembly methods on the output of workers at a fitness shoe factory. Two workers will be randomly assigned to each of four groups, for a total of eight in the study. Each worker will be given a headphone set so that the music type can be controlled. The number of shoes completed by each worker will be recorded. Does the kind of music or the assembly method or a combination of music and method affect output? The ANOVA model most likely to fit this situation is the two-way analysis of variance.

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Question 100

One-way ANOVA is applied to three independent samples having means 12, 15 and 20, respectively. If each observation in the third sample were increased by 40, the value of the F-statistic would increase by 40.

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

In ANOVA, a factor is an independent variable.

The following equation applies to which ANOVA model? SS(Total) = SST + SSE. A. One-way ANOVA B. Two-way ANOVA. C. Completely randomised design. D. Randomised block design.

Provide an example of a randomised block design with three treatments (k = 3) and four blocks (b = 4), in which SSB = 0 and SST and SSE are not equal to zero.

Which of the following is true of the F-distribution? A. It is skewed to the right. B. Its values are always positive. C. It is used in the ANOVA test. D. All of these choices are correct

In a completely randomised design for ANOVA, the numbers of degrees of freedom for the numerator and denominator are 3 and 25, respectively. The total number of observations must equal: A. 28. B. 25. C. 22. D. 29.

A partial ANOVA table in a randomised block design is shown below. Source of Variation SS df MS F Treatments * 3 * * Blocks 1256 2 * * Error * * 67.67 Total 2922 11 Can we infer at the 5% significance level that the block means differ?

The number of degrees of freedom for the denominator of a one-way ANOVA test for 5 population means with 12 observations sampled from each population is 55.

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 treatments is given by: A. $k-1$ . B. $n-k$ . C. $n-1$ . D. $n-k+1$ .

A partial ANOVA table in a randomised block design is shown below. Source of Variation SS df MS F Treatments * 3 * * Blocks 1256 2 * * Error * * 67.67 Total 2922 11 Can we infer at the 5% significance level that the treatment means differ?

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 likely false if: A. MST is much larger than MSE. B. MST is much smaller than MSE. C. MST is equal to MSE. D. MST is zero.

Given the significance level 0.05, the F-value for the numbers of degrees of freedom d.f. = (9, 6) is 4.10.

In a completely randomised 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. Source of Variation SS df MS F Treatments * * 240 * Error * * * Total 2512 *

Which of the following best describes an experimental design model where the treatments are defined as the levels of one factor, and the experimental design specifies independent samples? A. Randomised block design B. Two way ANOVA C. One way ANOVA D. All of these choices are correct.

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

One-way ANOVA is applied to three independent samples having means 12, 15 and 20, respectively. If each observation in the third sample were increased by 40, the value of the F-statistic would increase by 40.

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

In ANOVA, a factor is an independent variable.

The following equation applies to which ANOVA model? SS(Total) = SST + SSE. A. One-way ANOVA B. Two-way ANOVA. C. Completely randomised design. D. Randomised block design.

Provide an example of a randomised block design with three treatments (k = 3) and four blocks (b = 4), in which SSB = 0 and SST and SSE are not equal to zero.

Which of the following is true of the F-distribution? A. It is skewed to the right. B. Its values are always positive. C. It is used in the ANOVA test. D. All of these choices are correct

In a completely randomised design for ANOVA, the numbers of degrees of freedom for the numerator and denominator are 3 and 25, respectively. The total number of observations must equal: A. 28. B. 25. C. 22. D. 29.

A partial ANOVA table in a randomised block design is shown below. Source of Variation SS df MS F Treatments * 3 * * Blocks 1256 2 * * Error * * 67.67 Total 2922 11 Can we infer at the 5% significance level that the block means differ?

The number of degrees of freedom for the denominator of a one-way ANOVA test for 5 population means with 12 observations sampled from each population is 55.

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 treatments is given by: A. k−1 k-1 k−1 . B. n−k n-k n−k . C. n−1 n-1 n−1 . D. n−k+1 n-k+1 n−k+1 .

A partial ANOVA table in a randomised block design is shown below. Source of Variation SS df MS F Treatments * 3 * * Blocks 1256 2 * * Error * * 67.67 Total 2922 11 Can we infer at the 5% significance level that the treatment means differ?

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 likely false if: A. MST is much larger than MSE. B. MST is much smaller than MSE. C. MST is equal to MSE. D. MST is zero.

Given the significance level 0.05, the F-value for the numbers of degrees of freedom d.f. = (9, 6) is 4.10.

In a completely randomised 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. Source of Variation SS df MS F Treatments * * 240 * Error * * * Total 2512 *

Which of the following best describes an experimental design model where the treatments are defined as the levels of one factor, and the experimental design specifies independent samples? A. Randomised block design B. Two way ANOVA C. One way ANOVA D. All of these choices are correct.

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 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 treatments is given by: A. $k-1$ . B. $n-k$ . C. $n-1$ . D. $n-k+1$ .