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. $\begin{array}{ccc} \hline \text { Machine A } & \text { Machine B } & \text { Machine C } \\ \hline 11.8 & 11.7 & 12.2 \\ 12.1 & 11.9 & 12.1 \\ 12.0 & 11.7 & 12.0 \\ 11.9 & 11.8 & 11.9 \\ 12.1 & 12.0 & 12.2 \\ \hline \end{array}$ Is there a significant difference between the vending machines $\mathrm { A } , \mathrm { B }$, and $\mathrm { C }$ ? Use $\alpha = 0.05$

A) The $F$-test cannot be used to answer whether or not there is a significant difference between the means. B) No, there is no significant difference between the means. C) Yes, there is a significant difference between the means. A) The $F$-test cannot be used to answer whether or not there is a significant difference between the means. B) No, there is no significant difference between the means. C) Yes, there is a significant difference between the means.

A Two-Way ANOVA Summary Table is shown below. $\begin{array}{lrrrc} \text { Source } & {\text { SS }} & \text { d.f. } & \text { MS } & \text { F } \\ \text { Factor A } & 13.16 & 2 & 6.58 & 3.87 \\ \text { Factor B } & 6.94 & 2 & 3.47 & 2.04 \\ \text { Interaction A } \times \text { B } & 30.40 & 4 & 7.60 & 4.47 \\ \text { Within (error) } & 76.50 & 45 & 1.7 & \\ \text { Total } & 126.99 & 53 & & \end{array}$ The critical value for the $F$-test using $\alpha = 0.05$, d.f.N. $= 2$, and d.f.D $= 45$ is $3.20$. Then,

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

The following table shows the weekly total sales (in dollars) at a small roadside vegetable for the months June through September. $\begin{array}{ccccc} \hline \text { Month } &{\text { Weekly Sales }} \\ \hline \text { June } & 1132 & 791 & 1006 & 990 \\ \text { July } & 1060 & 1069 & 1007 & 1093 \\ \text { August } & 1181 & 1143 & 1248 & 1223 \\ \text { September } & 841 & 855 & 957 & 943 \\ \hline \end{array}$ Perform a Tukey test to determine which pairs of means, if any, differ. Use the $\alpha = 0.01$ le significance.

A) $\mu _ { \text {June } } \neq \mu _ { \text {Aug } } , \mu _ { \mathrm { Aug } } \neq \mu _ { \text {Sept } }$ B) $\mu _ { \text {July } } \neq \mu _ { \mathrm { Aug } }$ C) $\mu _ { \mathrm { Aug } } \neq \mu _ { \mathrm { Sept } }$ D) There is not enough evidence to conclude that any of the means differ. A) $\mu _ { \text {June } } \neq \mu _ { \text {Aug } } , \mu _ { \mathrm { Aug } } \neq \mu _ { \text {Sept } }$ B) $\mu _ { \text {July } } \neq \mu _ { \mathrm { Aug } }$ C) $\mu _ { \mathrm { Aug } } \neq \mu _ { \mathrm { Sept } }$ D) There is not enough evidence to conclude that any of the means differ.

A portion of an ANOVA summary table is shown below. $\begin{array} { l c c } \text { Source } & \text { Sum of Squares } & \text { Degrees of Freedom } \\ \text { Between } & 20 & 2 \\ \text { Within (error) } & 35 & 29 \\ \text { Total } & 55 \end{array}$ The critical value for this problem should have dfN (degrees of freedom in the numerator dfD (degrees of freedom in the denominator) of

A) dfN = 35, dfD = 20 B) dfN = 29, dfD = 2 C) dfN = 20, dfD = 35 D) dfN = 2, dfD = 29 A) dfN = 35, dfD = 20 B) dfN = 29, dfD = 2 C) dfN = 20, dfD = 35 D) dfN = 2, dfD = 29

Exam 12: Analysis of Variance

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 8 population means (from equal sized samples) are not all equal. We Should expect that

(Multiple Choice)

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Question 41

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubbeı content. $The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubbeı content. Can the mean effect of the rubber content be interpreted? If so, interpret the main effect. \alpha=0.01 level of significance.$ Can the mean effect of the rubber content be interpreted? If so, interpret the main effect. $\alpha=0.01$ level of significance.

(Multiple Choice)

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Question 42

The test can be used after the analysis of variance has been completed to make pairwise comparisons between means when groups have the same sample size.

(Short Answer)

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Question 43

A researcher is comparing 4 groups to test if they have the same means. There are data values altogether. The degrees of freedom for the Between (dfB) and the degrees of Freedom for the Within (dfW) are

(Multiple Choice)

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Question 44

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below. $An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below. i). Can you reject the hypothesis of no interactions? ii). Can the main effect of curing temperature (low or high) on bonding strength b interpreted? If so, interpret the main effect using the \alpha = 0.05 level of significance iii). Can the main effect of curing time on bonding strength be interpreted? If so, i the main effect using the \alpha = 0.05 level of significance.$ i). Can you reject the hypothesis of no interactions? ii). Can the main effect of curing temperature (low or high) on bonding strength b interpreted? If so, interpret the main effect using the $\alpha = 0.05$ level of significance iii). Can the main effect of curing time on bonding strength be interpreted? If so, i the main effect using the $\alpha = 0.05$ level of significance.

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Question 45

The test to detect where the difference is among the means can be used even if the sample sizes are not equal.

(Short Answer)

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Question 46

When finding the degrees of freedom for the $F$ -distribution, d. f. $\mathrm { N }$ is equal to one less than the number of groups.

(True/False)

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Question 47

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 6 , n _ { 2 } = 9$ , and $n _ { 3 } = 8$ . The sample means were $\bar { x } _ { 1 } = 1.52 , \bar { x } _ { 2 } = 1.62$ , and $\bar { x } _ { 3 } = 1.65$ . The sample standard deviations were $s _ { 1 } = 0.50 , s _ { 2 } = 0.36$ , and $s _ { 3 } = 0.48$ . The grand mean is $\bar { x } = 1.604348$ . Compute the value of the test statistic $F$ .

(Multiple Choice)

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Question 48

In 2-way ANOVA, effects of the independent variables are also referred to as the .

(Short Answer)

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Question 49

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

(Multiple Choice)

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Question 50

A researcher can use the Scheffé or Tukey test to determine where the difference in the means lies, once the null hypothesis for the $F$ -test has been rejected.

(True/False)

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Question 51

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 Is there a significant difference between the vending machines $\mathrm { A } , \mathrm { B }$ , and $\mathrm { C }$ ? Use $\alpha = 0.05$

(Multiple Choice)

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Question 52

A researcher is performing a two-way ANOVA using two factors. The first factor has levels and the second factor has 9 levels. In the ANOVA Summary Table, the degrees of Freedom for the interaction between the first and second factors will be

(Multiple Choice)

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Question 53

A Two-Way ANOVA Summary Table is shown below. Source SS d.f. MS F Factor A 13.16 2 6.58 3.87 Factor B 6.94 2 3.47 2.04 Interaction A \times B 30.40 4 7.60 4.47 Within (error) 76.50 45 1.7 Total 126.99 53 The critical value for the $F$ -test using $\alpha = 0.05$ , d.f.N. $= 2$ , and d.f.D $= 45$ is $3.20$ . Then,

(Multiple Choice)

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Question 54

The following table shows the weekly total sales (in dollars) at a small roadside vegetable for the months June through September. Month Weekly Sales June 1132 791 1006 990 July 1060 1069 1007 1093 August 1181 1143 1248 1223 September 841 855 957 943 Perform a Tukey test to determine which pairs of means, if any, differ. Use the $\alpha = 0.01$ le significance.

(Multiple Choice)

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Question 55

A portion of an ANOVA summary table is shown below. Source Sum of Squares Degrees of Freedom Between 20 2 Within (error) 35 29 Total 55 The critical value for this problem should have dfN (degrees of freedom in the numerator dfD (degrees of freedom in the denominator) of

(Multiple Choice)

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Question 56

An agricultural scientist performs a 2-way ANOVA to determine the effects of three diffe soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. following MINITAB output presents the results. Analysis of Variance for Sprouting Source DF SS MS F P Soil Mixture 2 8.296296 4.148148 2.871795 0.082706 Hybrid Variety 2 2.074074 1.037037 0.717949 0.5012 Interaction 4 5.037037 1.259259 0.871795 0.499899 Error 18 26 1.444444 Total 26 41.407407 Can you reject the hypothesis of no interactions?

(Multiple Choice)

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Question 57

The variance is made by computing the variance using all the data and is not affected by differences in the means.

(Short Answer)

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Question 58

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content. $The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content. Can the mean effect of the binder content be interpreted? If so, interpret the main effect. I \alpha=0.01 level of significance.$ Can the mean effect of the binder content be interpreted? If so, interpret the main effect. I $\alpha=0.01$ level of significance.

(Multiple Choice)

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Question 59

If there is no difference in the means, the variance will be approximately equal to the within-group variance.

(Short Answer)

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Question 60

Showing 41 - 60 of 69

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 8 population means (from equal sized samples) are not all equal. We Should expect that

The test can be used after the analysis of variance has been completed to make pairwise comparisons between means when groups have the same sample size.

A researcher is comparing 4 groups to test if they have the same means. There are data values altogether. The degrees of freedom for the Between (dfB) and the degrees of Freedom for the Within (dfW) are

The test to detect where the difference is among the means can be used even if the sample sizes are not equal.

When finding the degrees of freedom for the $F$ -distribution, d. f. $\mathrm { N }$ is equal to one less than the number of groups.

In 2-way ANOVA, effects of the independent variables are also referred to as the .

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

A researcher can use the Scheffé or Tukey test to determine where the difference in the means lies, once the null hypothesis for the $F$ -test has been rejected.

A researcher is performing a two-way ANOVA using two factors. The first factor has levels and the second factor has 9 levels. In the ANOVA Summary Table, the degrees of Freedom for the interaction between the first and second factors will be

A portion of an ANOVA summary table is shown below. Source Sum of Squares Degrees of Freedom Between 20 2 Within (error) 35 29 Total 55 The critical value for this problem should have dfN (degrees of freedom in the numerator dfD (degrees of freedom in the denominator) of

The variance is made by computing the variance using all the data and is not affected by differences in the means.

If there is no difference in the means, the variance will be approximately equal to 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

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 8 population means (from equal sized samples) are not all equal. We Should expect that

The test can be used after the analysis of variance has been completed to make pairwise comparisons between means when groups have the same sample size.

A researcher is comparing 4 groups to test if they have the same means. There are data values altogether. The degrees of freedom for the Between (dfB) and the degrees of Freedom for the Within (dfW) are

The test to detect where the difference is among the means can be used even if the sample sizes are not equal.

When finding the degrees of freedom for the FFF -distribution, d. f. N\mathrm { N }N is equal to one less than the number of groups.

In 2-way ANOVA, effects of the independent variables are also referred to as the .

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?

A researcher can use the Scheffé or Tukey test to determine where the difference in the means lies, once the null hypothesis for the FFF -test has been rejected.

A researcher is performing a two-way ANOVA using two factors. The first factor has levels and the second factor has 9 levels. In the ANOVA Summary Table, the degrees of Freedom for the interaction between the first and second factors will be

A portion of an ANOVA summary table is shown below. Source Sum of Squares Degrees of Freedom Between 20 2 Within (error) 35 29 Total 55 The critical value for this problem should have dfN (degrees of freedom in the numerator dfD (degrees of freedom in the denominator) of

The variance is made by computing the variance using all the data and is not affected by differences in the means.

If there is no difference in the means, the variance will be approximately equal to 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

When finding the degrees of freedom for the $F$ -distribution, d. f. $\mathrm { N }$ is equal to one less than the number of groups.

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

A researcher can use the Scheffé or Tukey test to determine where the difference in the means lies, once the null hypothesis for the $F$ -test has been rejected.