A random sample of 10 observations was selected from each of four normal populations. A partial one-way ANOVA table is shown below: \[\begin{array} { | l | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & d f & M S & F \\ \hline \text { Treatments } & * & * & 270 & * \\ \hline \text { Error } & * & * & * & \\ \hline \text { Total } & 1,350 & * & & \\ \hline \end{array}\] a. Complete the missing entries (identified by asterisks) in the ANOVA table. b. How many groups were in this study? c. How many experimental units were in this study? d. At the 5% significance level, can we infer that the means of the populations differ?

a. @#IMG-DLM& b. 4. c. 40. d. @#IMG-DLM& . @#IMG-DLM& At lea

In a two-tailed pooled-variance t-test (equal-variances t-test), the null and alternative hypotheses are exactly the same as in one-way ANOVA with: $\begin{array}{|l|l|} \hline \text { A. } & \text { exactly one treatment. } \\ \hline \text { B. } & \text { exactly two treatments. } \\ \hline \text { C. } & \text { exactly three treatments. } \\ \hline \text { D. } & \text { any number of treatments. } \\ \hline \end{array}$

The answer of In a two-tailed pooled-variance t-test (equal-variances t-test),...

The following statistics were calculated based on samples drawn from three normal populations: \[\begin{array} { | c | c | c | c | } \hline && { \text { Treatment } } \\ \hline \text { Statistic } & 1 & 2 & 3 \\ \hline n & 10 & 10 & 10 \\ \hline \bar { x } & 95 & 86 & 92 \\ \hline s & 10 & 12 & 15 \\ \hline \end{array}\] Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means.

Ho: µ 1 = µ 2 = µ 3 H A : At l

The following data are drawn from three normal populations. \[\begin{array} { | c | c | c | } \hline \mathrm { A } & \mathrm { B } & \mathrm { C } \\ \hline 5 & 8 & 16 \\ \hline 16 & 13 & 5 \\ \hline 13 & 12 & 10 \\ \hline 14 & 15 & 13 \\ \hline 10 & 23 & \\ \hline & 11 & \\ \hline \end{array}\] Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Assume that the random variable is normally distributed.

Ho: µ 1 = µ 2 = µ 3 H A : At least two means diffe

Exam 16: Analysis of Variance

The sum of squares for error (SSE) explains some of the total variation, while the sum of squares for treatments (SST) measures the amount of variation that is unexplained.

(True/False)

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Question 61

Given the significance level 0.025, the F-value for the numbers of degrees of freedom d.f. = (8, 10) is 3.85.

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Question 62

Two independent samples of size 30 each have been selected at random from the female and male students of a university. To test whether there is any difference in the grade point average between female and male students, an equal-variances t-test will be considered. Another test to consider is ANOVA. Which of the following is the most likely ANOVA to fit this test situation? A. Randomised block design. B. Two-way ANOVA. C. One-way ANOVA D. Chi-squared test.

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Question 63

In employing the randomised block design, the primary interest lies in reducing the within-treatments variation in order to make easier to detect differences between the treatment means.

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Question 64

We do not need the t-test of $\mu _ { 1 } - \mu _ { 2 }$ , since the analysis of variance can be used to test the difference between the two population means.

(True/False)

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Question 65

A random sample of 10 observations was selected from each of four normal populations. A partial one-way ANOVA table is shown below: Source of Variation SS df MS F Treatments * * 270 * Error * * * Total 1,350 * a. Complete the missing entries (identified by asterisks) in the ANOVA table. b. How many groups were in this study? c. How many experimental units were in this study? d. At the 5% significance level, can we infer that the means of the populations differ?

(Essay)

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Question 66

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.

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Question 67

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 68

In a one-way ANOVA where there are k treatments and n observations, the numbers of degrees of freedom for the F-statistic are equal to: A. $k-1$ and $n-1$ . B. $k-1$ and $n-k$ . C. $n-k$ and $k-1$ . D. $n k-1$ and $k-1$ .

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Question 69

The F-statistic in a one-way ANOVA represents the variation: A. between the treatments plus the variation within the treatments. B. within the treatments minus the variation between the treatments. C. between the treatments divided by the variation within the treatments. D. variation within the treatments divided by the variation between the treatments.

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Question 70

Three tennis players, one a beginner, one intermediate and one advanced, have been randomly selected from the membership of a club in a large city. Using the same tennis ball, each player hits ten serves, one with each of three racquet models, with the three racquet models selected randomly. The speed of each serve is measured with a machine and the result recorded. Among the ANOVA models listed below, the most likely model to fit this situation is the: A. one-way ANOVA. B. two-way ANOVA. C. randomised block design. D. matched-pairs model.

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Question 71

Which of the following statements is true? A. The sum of squares for treatments (SST) explains some of the variation. B. The sum of squares for error (SSE) measures the amount of variation that is unexplained. C. $\mathrm{SS}($ Total $)=\mathrm{SST}+\mathrm{SSE}$ D. All of these choices are correct.

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Question 72

If we first arrange test units into similar groups before assigning treatments to them, the test design we should use is the randomised block design.

(True/False)

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Question 73

The sum of squares for treatments stands for the between-treatments variation.

(True/False)

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Question 74

The distribution of the test statistic for analysis of variance is the F-distribution.

(True/False)

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Question 75

In a two-tailed pooled-variance t-test (equal-variances t-test), the null and alternative hypotheses are exactly the same as in one-way ANOVA with: A. exactly one treatment. B. exactly two treatments. C. exactly three treatments. D. any number of treatments.

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Question 76

The marketing management of a shopping complex food court, wants to investigate the average age of customers of three of the food court's fast food outlets: fish and chips, sandwich bar, and chicken and chips. This is to ascertain whether they should be providing different seating options for patrons. They take a random sample of eight customers at each of these three outlets and record their ages. Do these data provide enough evidence at the 5% significance level to infer that there are differences in ages among the customers of the fast food outlets, and that the food court should provide different seating options? From previous analyses, ages of customers of this food court are normally distributed.

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Question 77

A randomised block experiment having 5 treatments and 6 blocks produced the following values: SST = 252, SSB = 1095, SSE = 198. The value of SS(Total) must be 645.

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Question 78

The following statistics were calculated based on samples drawn from three normal populations: Treatment Statistic 1 2 3 n 10 10 10 95 86 92 s 10 12 15 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means.

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Question 79

The following data are drawn from three normal populations. 5 8 16 16 13 5 13 12 10 14 15 13 10 23 11 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Assume that the random variable is normally distributed.

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Question 80

The sum of squares for error (SSE) explains some of the total variation, while the sum of squares for treatments (SST) measures the amount of variation that is unexplained.

Given the significance level 0.025, the F-value for the numbers of degrees of freedom d.f. = (8, 10) is 3.85.

In employing the randomised block design, the primary interest lies in reducing the within-treatments variation in order to make easier to detect differences between the treatment means.

We do not need the t-test of $\mu _ { 1 } - \mu _ { 2 }$ , since the analysis of variance can be used to test the difference between the two population means.

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.

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

In a one-way ANOVA where there are k treatments and n observations, the numbers of degrees of freedom for the F-statistic are equal to: A. $k-1$ and $n-1$ . B. $k-1$ and $n-k$ . C. $n-k$ and $k-1$ . D. $n k-1$ and $k-1$ .

Which of the following statements is true? A. The sum of squares for treatments (SST) explains some of the variation. B. The sum of squares for error (SSE) measures the amount of variation that is unexplained. C. $\mathrm{SS}($ Total $)=\mathrm{SST}+\mathrm{SSE}$ D. All of these choices are correct.

If we first arrange test units into similar groups before assigning treatments to them, the test design we should use is the randomised block design.

The sum of squares for treatments stands for the between-treatments variation.

The distribution of the test statistic for analysis of variance is the F-distribution.

In a two-tailed pooled-variance t-test (equal-variances t-test), the null and alternative hypotheses are exactly the same as in one-way ANOVA with: A. exactly one treatment. B. exactly two treatments. C. exactly three treatments. D. any number of treatments.

A randomised block experiment having 5 treatments and 6 blocks produced the following values: SST = 252, SSB = 1095, SSE = 198. The value of SS(Total) must be 645.

The following statistics were calculated based on samples drawn from three normal populations: Treatment Statistic 1 2 3 n 10 10 10 95 86 92 s 10 12 15 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means.

The following data are drawn from three normal populations. 5 8 16 16 13 5 13 12 10 14 15 13 10 23 11 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Assume that the random variable is normally distributed.

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 error (SSE) explains some of the total variation, while the sum of squares for treatments (SST) measures the amount of variation that is unexplained.

Given the significance level 0.025, the F-value for the numbers of degrees of freedom d.f. = (8, 10) is 3.85.

In employing the randomised block design, the primary interest lies in reducing the within-treatments variation in order to make easier to detect differences between the treatment means.

We do not need the t-test of μ1−μ2\mu _ { 1 } - \mu _ { 2 }μ1​−μ2​ , since the analysis of variance can be used to test the difference between the two population means.

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.

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

If we first arrange test units into similar groups before assigning treatments to them, the test design we should use is the randomised block design.

The sum of squares for treatments stands for the between-treatments variation.

The distribution of the test statistic for analysis of variance is the F-distribution.

In a two-tailed pooled-variance t-test (equal-variances t-test), the null and alternative hypotheses are exactly the same as in one-way ANOVA with: A. exactly one treatment. B. exactly two treatments. C. exactly three treatments. D. any number of treatments.

A randomised block experiment having 5 treatments and 6 blocks produced the following values: SST = 252, SSB = 1095, SSE = 198. The value of SS(Total) must be 645.

The following statistics were calculated based on samples drawn from three normal populations: Treatment Statistic 1 2 3 n 10 10 10 95 86 92 s 10 12 15 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means.

The following data are drawn from three normal populations. 5 8 16 16 13 5 13 12 10 14 15 13 10 23 11 Set up the ANOVA table and test at the 5% level of significance to determine whether differences exist among the population means. Assume that the random variable is normally distributed.

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

We do not need the t-test of $\mu _ { 1 } - \mu _ { 2 }$ , since the analysis of variance can be used to test the difference between the two population means.

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.