A Two-Way ANOVA Summary Table is shown below. $\begin{array}{lrrcc} \text { Source } & {\mathrm{SS}} & \text { d.f. } & \text { MS } & \text { F } \\ \text { Factor A } & 13.97 & 2 & 6.99 & 4.99 \\ \text { Factor B } & 3.67 & 2 & 1.83 & 1.31 \\ \text { Interaction A } \times \text { B } & 10.81 & 4 & 2.70 & 1.93 \\ \text { Within (error) } & 50.40 & 36 & 1.4 & \\ \text { Total } & 78.848 & 44 & & \end{array}$ The critical value for the $F$-test using $\alpha = 0.05$, d.f.N. $= 2$, and d.f.D $= 36$ is $3.26$. Then,

A) only the null hypothesis concerning Factor A and the Interaction (A × B) effect should be rejected. B) only the null hypothesis concerning Factor A should be rejected. C) only the null hypothesis concerning Factor B should be rejected. D) all of the null hypotheses should be accepted. A) only the null hypothesis concerning Factor A and the Interaction (A × B) effect should be rejected. B) only the null hypothesis concerning Factor A should be rejected. C) only the null hypothesis concerning Factor B should be rejected. D) all of the null hypotheses should be accepted.

A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Their data is given below. $\begin{array}{ccc} \hline \text { Machine A } & \text { Machine B } & \text { Machine C } \\ \hline 11.8 & 11.7 & 12.2 \\ 12.1 & 11.9 & 12.1 \\ 12.0 & 11.7 & 12.0 \\ 11.9 & 11.8 & 11.9 \\ 12.1 & 12.0 & 12.2 \\ \hline \end{array}$ Compute the test value for the coffee machines.

A) 5.06 B) 2.25 C) 4.86 D) 6.62 A) 5.06 B) 2.25 C) 4.86 D) 6.62

Exam 12: Analysis of Variance

The following table presents measurements of the tensile strength (in kilopascals) asphalt-rubber concrete beams for three levels of binder content and three levels o rubber content. $The following table presents measurements of the tensile strength (in kilopascals) asphalt-rubber concrete beams for three levels of binder content and three levels o rubber content. i). Can you reject the hypothesis of no interactions? ii). Can the mean effect of the binder content be interpreted? If so, interpret the m effect. Use the \alpha = 0.01 level of significance. iii). Can the mean effect of the rubber content be interpreted? If so, interpret the \mathrm { m } effect. Use the \alpha = 0.01 level of significance.$ i). Can you reject the hypothesis of no interactions? ii). Can the mean effect of the binder content be interpreted? If so, interpret the $m$ effect. Use the $\alpha = 0.01$ level of significance. iii). Can the mean effect of the rubber content be interpreted? If so, interpret the $\mathrm { m }$ effect. Use the $\alpha = 0.01$ level of significance.

(Essay)

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Question 61

The following table shows the weekly total sales (in dollars) at a small roadside vegetable stand for the months June through September. Month Weekly Sales June 983 1105 1012 1004 July 1054 940 1119 1065 August 1054 1088 1139 1107 September 1081 827 960 951 Can you conclude that the weekly sales varies with the month? Use the $\alpha = 0.05$ level of significance.

(Multiple Choice)

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Question 62

In a two-way ANOVA design, variable A has four levels and variable B has two levels. There are eight data values in each cell. What is the d.f.N. for factor B?

(Short Answer)

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Question 63

$\text { The figure below is an example of what type of interaction? }$ $\text { The figure below is an example of what type of interaction? }$

(Multiple Choice)

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Question 64

For three groups, the $F$ -test can show whether or not a difference exists among three means and where the difference lies.

(True/False)

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Question 65

A Two-Way ANOVA Summary Table is shown below. Source d.f. MS F Factor A 13.97 2 6.99 4.99 Factor B 3.67 2 1.83 1.31 Interaction A \times B 10.81 4 2.70 1.93 Within (error) 50.40 36 1.4 Total 78.848 44 The critical value for the $F$ -test using $\alpha = 0.05$ , d.f.N. $= 2$ , and d.f.D $= 36$ is $3.26$ . Then,

(Multiple Choice)

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Question 66

In the Tukey test, if $\bar { X } _ { 2 } = 8$ for a group size $n _ { 2 } = 8 , \bar { X } _ { 4 } = 12$ for a group size $n _ { 4 }$ and the within-group variance $s _ { w } ^ { 2 } = 24$ , then the $q$ test value for comparing group 2 to group 4 is

(Multiple Choice)

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Question 67

A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Their data is given below. Machine A Machine B Machine C 11.8 11.7 12.2 12.1 11.9 12.1 12.0 11.7 12.0 11.9 11.8 11.9 12.1 12.0 12.2 Compute the test value for the coffee machines.

(Multiple Choice)

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Question 68

When performing an $F$ -test, if the means differ significantly, the between-group variance will be much smaller than the within-group variance.

(True/False)

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Question 69

Showing 61 - 69 of 69

In a two-way ANOVA design, variable A has four levels and variable B has two levels. There are eight data values in each cell. What is the d.f.N. for factor B?

$\text { The figure below is an example of what type of interaction? }$ $\text { The figure below is an example of what type of interaction? }$

For three groups, the $F$ -test can show whether or not a difference exists among three means and where the difference lies.

In the Tukey test, if $\bar { X } _ { 2 } = 8$ for a group size $n _ { 2 } = 8 , \bar { X } _ { 4 } = 12$ for a group size $n _ { 4 }$ and the within-group variance $s _ { w } ^ { 2 } = 24$ , then the $q$ test value for comparing group 2 to group 4 is

When performing an $F$ -test, if the means differ significantly, the between-group variance will be much smaller than the within-group variance.

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Nonparametric Statistics

Sampling and Simulation

Filters

Exam 12: Analysis of Variance

In a two-way ANOVA design, variable A has four levels and variable B has two levels. There are eight data values in each cell. What is the d.f.N. for factor B?

The figure below is an example of what type of interaction? \text { The figure below is an example of what type of interaction? } The figure below is an example of what type of interaction?

For three groups, the FFF -test can show whether or not a difference exists among three means and where the difference lies.

When performing an FFF -test, if the means differ significantly, the between-group variance will be much smaller than the within-group variance.

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Nonparametric Statistics

Sampling and Simulation

Filters

$\text { The figure below is an example of what type of interaction? }$ $\text { The figure below is an example of what type of interaction? }$

For three groups, the $F$ -test can show whether or not a difference exists among three means and where the difference lies.

When performing an $F$ -test, if the means differ significantly, the between-group variance will be much smaller than the within-group variance.