The following table shows the average weekly losses of worker hours due to accidents in 2009 at five randomly selected manufacturing firms in New South Wales and at five randomly selected manufacturing firms in Victoria. \[\begin{array} { | c | c | } \hline \text { NSW } & \text { Victoria } \\ \hline 45 & 57 \\ \hline 73 & 83 \\ \hline 46 & 34 \\ \hline 124 & 26 \\ \hline 33 & 17 \\ \hline \end{array}\] Assume that the weekly losses of worker hours are normally distributed. Perform an equal-variances t-test at the 5% significance level to determine whether the population means differ.

@#LAT-DLM& . @#LAT-DLM& . Rejection region: | t |

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.

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

One-way ANOVA is performed on three independent samples with n1 = 10, n2 = 8 and n3 = 9. The critical value obtained from the F-table for this test at the 5% level of significance equals:

A) 39.46. B) 3.40. C) 4.32. D) 19.45. A) 39.46. B) 3.40. C) 4.32. D) 19.45.

Exam 16: Analysis of Variance

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.

(True/False)

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Question 81

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

(True/False)

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Question 82

An investor studied the percentage rates of return of three different types of mutual funds. Random samples of percentage rates of return for four periods were taken from each fund. The results appear in the table below. $\text { Mutual Funds Percentage Rates }$ Fund 1 Fund 2 Fund 3 12 4 9 15 8 3 13 6 5 14 5 7 17 4 4 Use Tukey's method with $\alpha$ =.05 to determine which population means differ.

(Essay)

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Question 83

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:

(Multiple Choice)

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Question 84

The F-statistic in a one-way ANOVA represents the variation:

(Multiple Choice)

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Question 85

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

(True/False)

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Question 86

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

(True/False)

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Question 87

The following table shows the average weekly losses of worker hours due to accidents in 2009 at five randomly selected manufacturing firms in New South Wales and at five randomly selected manufacturing firms in Victoria. NSW Victoria 45 57 73 83 46 34 124 26 33 17 Assume that the weekly losses of worker hours are normally distributed. Perform an equal-variances t-test at the 5% significance level to determine whether the population means differ.

(Essay)

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Question 88

When the response is not normally distributed, we can replace the randomised block ANOVA with its non-parametric counterpart; the Friedman test.

(True/False)

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Question 89

In ANOVA, the F-test is the ratio of two sample variances. In the one-way ANOVA (completely randomised design), the variance used as the denominator of the ratio is the:

(Multiple Choice)

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Question 90

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.

(Essay)

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Question 91

One-way ANOVA is applied to three independent samples having means 10, 13 and 18, respectively. If each observation in the first sample were decreased by 5, the value of the F-statistic would:

(Multiple Choice)

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Question 92

The objective of designing a randomized block experiment is to decrease the within-treatments variation to detect differences between the treatment means.

(True/False)

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Question 93

The calculated value of F in a one-way analysis is 7.88. The numbers of degrees of freedom for numerator and denominator are 3 and 9, respectively. The most accurate statement to be made about the p-value is that p-value < 0.01.

(True/False)

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Question 94

In one-way analysis of variance, within-treatments variation stands for the:

(Multiple Choice)

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Question 95

One-way ANOVA is performed on three independent samples with n₁= 10, n₂= 8 and n₃= 9. The critical value obtained from the F-table for this test at the 5% level of significance equals:

(Multiple Choice)

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Question 96

Tukey's multiple comparison method determines a critical number, $\omega$ ; such that if any pair of sample means has a difference smaller than $\omega$ , we conclude that the pair's two corresponding population means are different.

(True/False)

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Question 97

In one-way ANOVA, the amount of total variation that is unexplained is measured by the:

(Multiple Choice)

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Question 98

A survey is to be conducted to compare the superannuation contributions made by employees from three Victorian universities. Employees are to be randomly selected from each of the three universities and the dollar amounts of their contributions recorded. The ANOVA model most likely to fit this situation is the randomised block design.

(True/False)

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Question 99

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.

(True/False)

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Question 100

Showing 81 - 100 of 115

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.

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

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:

The F-statistic in a one-way ANOVA represents the variation:

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

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

When the response is not normally distributed, we can replace the randomised block ANOVA with its non-parametric counterpart; the Friedman test.

In ANOVA, the F-test is the ratio of two sample variances. In the one-way ANOVA (completely randomised design), the variance used as the denominator of the ratio is the:

One-way ANOVA is applied to three independent samples having means 10, 13 and 18, respectively. If each observation in the first sample were decreased by 5, the value of the F-statistic would:

The objective of designing a randomized block experiment is to decrease the within-treatments variation to detect differences between the treatment means.

The calculated value of F in a one-way analysis is 7.88. The numbers of degrees of freedom for numerator and denominator are 3 and 9, respectively. The most accurate statement to be made about the p-value is that p-value < 0.01.

In one-way analysis of variance, within-treatments variation stands for the:

One-way ANOVA is performed on three independent samples with n₁= 10, n₂= 8 and n₃= 9. The critical value obtained from the F-table for this test at the 5% level of significance equals:

Tukey's multiple comparison method determines a critical number, $\omega$ ; such that if any pair of sample means has a difference smaller than $\omega$ , we conclude that the pair's two corresponding population means are different.

In one-way ANOVA, the amount of total variation that is unexplained is measured by the:

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

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.

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

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:

The F-statistic in a one-way ANOVA represents the variation:

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

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

When the response is not normally distributed, we can replace the randomised block ANOVA with its non-parametric counterpart; the Friedman test.

In ANOVA, the F-test is the ratio of two sample variances. In the one-way ANOVA (completely randomised design), the variance used as the denominator of the ratio is the:

One-way ANOVA is applied to three independent samples having means 10, 13 and 18, respectively. If each observation in the first sample were decreased by 5, the value of the F-statistic would:

The objective of designing a randomized block experiment is to decrease the within-treatments variation to detect differences between the treatment means.

The calculated value of F in a one-way analysis is 7.88. The numbers of degrees of freedom for numerator and denominator are 3 and 9, respectively. The most accurate statement to be made about the p-value is that p-value < 0.01.

In one-way analysis of variance, within-treatments variation stands for the:

One-way ANOVA is performed on three independent samples with n1 = 10, n2 = 8 and n3 = 9. The critical value obtained from the F-table for this test at the 5% level of significance equals:

Tukey's multiple comparison method determines a critical number, ω\omegaω ; such that if any pair of sample means has a difference smaller than ω\omegaω , we conclude that the pair's two corresponding population means are different.

In one-way ANOVA, the amount of total variation that is unexplained is measured by the:

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

One-way ANOVA is performed on three independent samples with n₁= 10, n₂= 8 and n₃= 9. The critical value obtained from the F-table for this test at the 5% level of significance equals:

Tukey's multiple comparison method determines a critical number, $\omega$ ; such that if any pair of sample means has a difference smaller than $\omega$ , we conclude that the pair's two corresponding population means are different.