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. $\begin{array} { | c | c | c | } \hline & { \text { Mutual Funds Percentage Rates } } \\ \hline \text { Fund } 1 & \text { Fund } 2 & \text { Fund } 3 \\ \hline 12 & 4 & 9 \\ \hline 15 & 8 & 3 \\ \hline 13 & 6 & 5 \\ \hline 14 & 5 & 7 \\ \hline 17 & 4 & 4 \\ \hline \end{array}$ Use Tukey's method with \[\alpha\] =.05 to determine which population means differ.

@#IMG-DLM& = 2.684 @#IMG-DLM& It is clear that the

In order to examine the differences in age of teachers among five school districts, an educational statistician took random samples of six teachers' ages in each district. The data are listed below. $\text { Ages of teachers am ong five school districts }$ $\begin{array} { | c | c | c | c | c | } \hline 1 & 2 & 3 & 4 & 5 \\ \hline 42 & 23 & 45 & 31 & 37 \\ \hline 22 & 52 & 48 & 45 & 40 \\ \hline 33 & 32 & 50 & 33 & 45 \\ \hline 32 & 44 & 45 & 38 & 61 \\ \hline 26 & 39 & 37 & 29 & 50 \\ \hline 24 & 33 & 49 & 46 & 50 \\ \hline \end{array}$ Assume that ages of teachers are normally distributed. Test at the 5% significance level to determine whether differences in teachers' ages exist among the five districts.

@#IMG-DLM& @#IMG-DLM& At least two means differ. @#IMG-DLM&

A randomised block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1951, SSB = 1414.4, SSE = 188. The value of SST must be: $\begin{array}{|l|l|} \hline \text { A. } & 99 . \\ \hline \text { B. } & 3553 . \\ \hline \text { C. } & 349 . \\ \hline \text { D. } & \text { None of these choices are correct. } \\ \hline \end{array}$

The answer of A randomised block design with 4 treatments...

The randomised block design with exactly two treatments is equivalent to a two-tailed: $\begin{array}{|l|l|} \hline A.&\text { independent samples \( z $-test.}\\ \hline B.&\text { independent-samples equal-variances $ t $-test. }\\ \hline C.&\text {independent-samples unequal -variances $ t $-test. }\\ \hline D.&\text {matched pairs $ t $-test. }\\ \hline \end{array}\)

The answer of The randomised block design with exactly two...

Which of the following is a correct formulation for the null hypothesis in one-way ANOVA? $\begin{array}{|l|l|} \hline\text { A. } & \mu_{1}+\mu_{2}+\mu_{3}=0 \\ \hline \text { B. } & \mu_{1}+\mu_{2}+\mu_{3} \neq 0 \\ \hline \text { C. } & \mu_{1}=\mu_{2}=\mu_{3} \\ \hline \text { D. } & \mu_{1} \neq \mu_{2} \neq \mu_{3}\\\hline \end{array}$

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

Exam 16: Analysis of Variance

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: A. mean square for treatments. B. mean square for error. C. mean square for blocks. D. total sum of squares.

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Question 1

Correct Answer:

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B

A survey will be conducted to compare the grade point averages of US high-school students from four different school districts. Students are to be randomly selected from each of the four districts and their grade point averages recorded. The ANOVA model most likely to fit this situation is: A. one-way ANOVA. B. two-way ANOVA. C. randomised block design. D. complete 4 f factorial design.

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Question 2

Correct Answer:

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A

One-way ANOVA is performed on independent samples taken from three normally distributed populations with equal variances. The following summary statistics are calculated: $n _ { 1 } =$ 6, $\bar { x } _ { 1 } =$ 50, $s _ { 1 } =$ 5.2. $n _ { 2 } =$ 8, $\bar { x } _ { 2 } =$ 55, $s _ { 2 } =$ 4.9 . $n _ { 3 } =$ 6, $\bar { x } _ { 3 } =$ 51, $s _ { 3 } =$ 5.4. The grand mean equals: A. 50.0 B. 52.0 C. 52.3 D. 53.0

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Question 3

Correct Answer:

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C

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: A. increase. B. decrease. C. remain unchanged. D. decrease by 5 .

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Question 4

Is it possible to have a randomised block design of the analysis of variance in which SSE = 0 and SSB is not equal to zero? Explain.

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Question 5

In one-way ANOVA, the test statistic is defined as the ratio of the mean square for treatments (MST), over the mean square for error (MSE)that is, F = MST / MSE.

(True/False)

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Question 6

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. 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.

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Question 7

A professor of statistics at Wayne State University in the US wants to determine whether the average starting salaries among graduates of the 15 universities in Michigan are equal. A sample of 25 recent graduates from each university is randomly taken. The appropriate critical value for the ANOVA test is obtained from the F-distribution with number so of degrees of freedom equal to: A. 15 and 25. B. 14 and 360. C. 360 and 14. D. 25 and 15.

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Question 8

When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called one-way analysis of variance.

(True/False)

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Question 9

The randomised block design is also called the two-way analysis of variance.

(True/False)

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Question 10

In order to examine the differences in age of teachers among five school districts, an educational statistician took random samples of six teachers' ages in each district. The data are listed below. $\text { Ages of teachers am ong five school districts }$ 1 2 3 4 5 42 23 45 31 37 22 52 48 45 40 33 32 50 33 45 32 44 45 38 61 26 39 37 29 50 24 33 49 46 50 Assume that ages of teachers are normally distributed. Test at the 5% significance level to determine whether differences in teachers' ages exist among the five districts.

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Question 11

A recent college graduate is in the process of deciding which one of three US graduate schools he should apply to. He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school. A random sample of six students in each school produced the following GMAT scores. GMAT Scores School 1 School 2 School 3 650 510 590 620 550 510 630 700 520 580 630 500 710 600 490 690 650 530 Use Tukey's method with $\alpha$ =0.05 to determine which population means differ.

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Question 12

A randomised block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1951, SSB = 1414.4, SSE = 188. The value of SST must be: A. 99. B. 3553. C. 349. D. None of these choices are correct.

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Question 13

The randomised block design with exactly two treatments is equivalent to a two-tailed: A. independent samples z -test. B. independent-samples equal-variances t -test. C. independent-samples unequal -variances t -test. D. matched pairs t -test.

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Question 14

Which of the following is a correct formulation for the null hypothesis in one-way ANOVA? A. ++=0 B. ++0 C. == D.

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Question 15

In one-way ANOVA, the total variation SS(Total) is partitioned into three sources of variation: the sum of squares for treatments (SST), the sum of squares for blocks (SSB) and the sum of squares for error (SSE).

(True/False)

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Question 16

The F-statistic in a one-way ANOVA represents the variation between the treatments divided by the variation within the treatments.

(True/False)

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Question 17

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.

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Question 18

In one-way ANOVA, the amount of total variation that is unexplained is measured by the: A. sum of squares for treatments. B. sum of squares for error. C. total sum of squares. D. number of degrees of freedom.

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Question 19

The sum of squares for treatments, SST, achieves its smallest value (zero) when all the sample sizes are equal.

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Question 20

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: A. mean square for treatments. B. mean square for error. C. mean square for blocks. D. total sum of squares.

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: A. increase. B. decrease. C. remain unchanged. D. decrease by 5 .

Is it possible to have a randomised block design of the analysis of variance in which SSE = 0 and SSB is not equal to zero? Explain.

In one-way ANOVA, the test statistic is defined as the ratio of the mean square for treatments (MST), over the mean square for error (MSE)that is, F = MST / MSE.

When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called one-way analysis of variance.

The randomised block design is also called the two-way analysis of variance.

A randomised block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1951, SSB = 1414.4, SSE = 188. The value of SST must be: A. 99. B. 3553. C. 349. D. None of these choices are correct.

The randomised block design with exactly two treatments is equivalent to a two-tailed: A. independent samples z -test. B. independent-samples equal-variances t -test. C. independent-samples unequal -variances t -test. D. matched pairs t -test.

Which of the following is a correct formulation for the null hypothesis in one-way ANOVA? A. ++=0 B. ++0 C. == D.

In one-way ANOVA, the total variation SS(Total) is partitioned into three sources of variation: the sum of squares for treatments (SST), the sum of squares for blocks (SSB) and the sum of squares for error (SSE).

The F-statistic in a one-way ANOVA represents the variation between the treatments divided by the variation within the treatments.

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: A. sum of squares for treatments. B. sum of squares for error. C. total sum of squares. D. number of degrees of freedom.

The sum of squares for treatments, SST, achieves its smallest value (zero) when all the sample sizes are equal.

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

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: A. mean square for treatments. B. mean square for error. C. mean square for blocks. D. total sum of squares.

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: A. increase. B. decrease. C. remain unchanged. D. decrease by 5 .

Is it possible to have a randomised block design of the analysis of variance in which SSE = 0 and SSB is not equal to zero? Explain.

In one-way ANOVA, the test statistic is defined as the ratio of the mean square for treatments (MST), over the mean square for error (MSE)that is, F = MST / MSE.

When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called one-way analysis of variance.

The randomised block design is also called the two-way analysis of variance.

A randomised block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1951, SSB = 1414.4, SSE = 188. The value of SST must be: A. 99. B. 3553. C. 349. D. None of these choices are correct.

The randomised block design with exactly two treatments is equivalent to a two-tailed: A. independent samples z -test. B. independent-samples equal-variances t -test. C. independent-samples unequal -variances t -test. D. matched pairs t -test.

Which of the following is a correct formulation for the null hypothesis in one-way ANOVA? A. ++=0 B. ++0 C. == D.

In one-way ANOVA, the total variation SS(Total) is partitioned into three sources of variation: the sum of squares for treatments (SST), the sum of squares for blocks (SSB) and the sum of squares for error (SSE).

The F-statistic in a one-way ANOVA represents the variation between the treatments divided by the variation within the treatments.

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: A. sum of squares for treatments. B. sum of squares for error. C. total sum of squares. D. number of degrees of freedom.

The sum of squares for treatments, SST, achieves its smallest value (zero) when all the sample sizes are equal.

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

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.