Part of an ANOVA table is shown below. \[\begin{array} { l l l l l } \text { Source of } & \text { Sum of } & \text { Degrees of } & \text { Mean } \\ \text { Variation } & \text { Squares } & \text { Freedom } & \text { Square } & F \\ \text { Between Treatments } & 64 & &&8 \\ \text { Within Treatments (Error) } & &&2 & \\ \text { TOTAL } &100 \end{array}\] The mean square due to treatments (MSTR) is

A) 36. B) 16. C) 64. D) 15. A) 36. B) 16. C) 64. D) 15.

Consider the following ANOVA table. $\begin{array}{llll} \begin{array}{l} \text { Source } \\ \text { of Variation } \end{array} & \begin{array}{l} \text { Sum } \\ \text { of Squares } \end{array} & \begin{array}{l} \text { Degrees } \\ \text { of Freed om } \end{array} & \begin{array}{l} \text { Mean } \\ \text { Square } \end{array}&F \\ \text { Between Treatments } & 2073.6 & 4 & \\ \text { Between Blocks } & 6000 & 5 & 1200 \\ \text { Error } & & 20 & 288 \\ \text { Total } & & 29 & \end{array}$ The test statistic to test the null hypothesis equals

A) .432. B) 1.8. C) 4.17. D) 28.8. A) .432. B) 1.8. C) 4.17. D) 28.8.

Part of an ANOVA table is shown below. \[\begin{array} { l l l l l } \text { Source of } & \text { Sum of } & \text { Degrees of } & \text { Mean } \\ \text { Variation } & \text { Squares } & \text { Freedom } & \text { Square } & F \\ \text { Between Treatments } & 64 & &&8 \\ \text { Within Treatments (Error) } & &&2 & \\ \text { TOTAL } &100 \end{array}\] The number of degrees of freedom corresponding to between-treatments is

A) 18. B) 2. C) 4. D) 3. A) 18. B) 2. C) 4. D) 3.

Consider the following ANOVA table. $\begin{array}{llll} \begin{array}{l} \text { Source } \\ \text { of Variation } \end{array} & \begin{array}{l} \text { Sum } \\ \text { of Squares } \end{array} & \begin{array}{l} \text { Degrees } \\ \text { of Freed om } \end{array} & \begin{array}{l} \text { Mean } \\ \text { Square } \end{array}&F \\ \text { Between Treatments } & 2073.6 & 4 & \\ \text { Between Blocks } & 6000 & 5 & 1200 \\ \text { Error } & & 20 & 288 \\ \text { Total } & & 29 & \end{array}$ The null hypothesis is to be tested at the 5% level of significance.The p-value is

A) greater than .10. B) between .05 to .10. C) between .025 to .05. D) less than .01. A) greater than .10. B) between .05 to .10. C) between .025 to .05. D) less than .01.

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below. $\begin{array}{lllll} \text { Treatment } &&{\text { Observations }} \\ \text { A } & 20 & 30 & 25 & 33 \\ \text { B } & 22 & 26 & 20 & 28 \\ \mathrm{C} & 40 & 30 & 28 & 22 \end{array}$ The null hypothesis for this ANOVA problem is

A) $\mu$1 = $\mu$2. B) $\mu$1 = $\mu$2 = $\mu$3. C) $\mu$1 = $\mu$2 = $\mu$3 = $\mu$4. D) $\mu$1 = $\mu$2 = ... = $\mu$12. A) $\mu$1 = $\mu$2. B) $\mu$1 = $\mu$2 = $\mu$3. C) $\mu$1 = $\mu$2 = $\mu$3 = $\mu$4. D) $\mu$1 = $\mu$2 = ... = $\mu$12.

Consider the following information. $\begin{array}{ll} \mathrm{SSTR}=6750 & H 0: \mu 1=\mu 2=\mu 3=\mu 4 \\ \mathrm{SSE}=8000 & H_{\mathrm{a}}: \text { At least one mean is different } \end{array}$ The mean square due to treatments (MSTR) equals

A) 400. B) 500. C) 1687.5. D) 2250. A) 400. B) 500. C) 1687.5. D) 2250.

Part of an ANOVA table is shown below. \[\begin{array} { l l l l l } \text { Source of } & \text { Sum of } & \text { Degrees of } & \text { Mean } \\ \text { Variation } & \text { Squares } & \text { Freedom } & \text { Square } & F \\ \text { Between Treatments } & 64 & &&8 \\ \text { Within Treatments (Error) } & &&2 & \\ \text { TOTAL } &100 \end{array}\] If we want to determine whether or not the means of the populations are equal, the p-value is

A) greater than .1. B) between .05 to .1. C) between .025 to .05. D) less than .01. A) greater than .1. B) between .05 to .1. C) between .025 to .05. D) less than .01.

In a completely randomized design involving four treatments, the following information is provided. \[\begin{array}{ l cccc } &\text { Treatment } 1 &\text { Treatment } 2&\text { Treatment } 3& \text { Treatment } 4\\ \text { Sample Size } & 50 & 18 & 15 & 17 \\ \text { Sample Mean } & 32 & 38 & 42 & 48 \end{array}\] The overall mean (the grand mean) for all treatments is

A) 40.0. B) 37.3. C) 48.3. D) 37.0. A) 40.0. B) 37.3. C) 48.3. D) 37.0.

Part of an ANOVA table is shown below. \[\begin{array} { l l l l l } \text { Source of } & \text { Sum of } & \text { Degrees of } & \text { Mean } \\ \text { Variation } & \text { Squares } & \text { Freedom } & \text { Square } & F \\ \text { Between Treatments } & 64 & &&8 \\ \text { Within Treatments (Error) } & &&2 & \\ \text { TOTAL } &100 \end{array}\] At a 5% level of significance, if we want to determine whether or not the means of the populations are equal, the conclusion of the test is that

A) all means are equal. B) some means may be equal. C) not all means are equal. D) some means will never be equal. A) all means are equal. B) some means may be equal. C) not all means are equal. D) some means will never be equal.

Part of an ANOVA table is shown below. \[\begin{array} { l l l l l } \text { Source of } & \text { Sum of } & \text { Degrees of } & \text { Mean } \\ \text { Variation } & \text { Squares } & \text { Freedom } & \text { Square } & F \\ \text { Between Treatments } & 180 & 3 & \\ \text { Within Treatments (Error) } & & & \\ \text { TOTAL } & 480 & 18 & \end{array}\] The mean square due to treatments (MSTR) is

A) 20. B) 60. C) 18. D) 15. A) 20. B) 60. C) 18. D) 15.

Exam 13: Experimental Design and Analysis of Variance

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 64 8 Within Treatments (Error) 2 TOTAL 100 The mean square due to treatments (MSTR) is

(Multiple Choice)

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Question 21

The process of using the same or similar experimental units for all treatments is called

(Multiple Choice)

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Question 22

The required condition for using an ANOVA procedure on data from several populations is that the

(Multiple Choice)

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Question 23

Consider the following ANOVA table. Source of Variation Sum of Squares Degrees of Freed om Mean Square F Between Treatments 2073.6 4 Between Blocks 6000 5 1200 Error 20 288 Total 29 The test statistic to test the null hypothesis equals

(Multiple Choice)

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Question 24

The ANOVA procedure is a statistical approach for determining whether or not the means of

(Multiple Choice)

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Question 25

In an ANOVA procedure, a term that means the same as the term "variable" is

(Multiple Choice)

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Question 26

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations).Also, the design provided the following information. SSTR = 200 (Sum of Squares Due to Treatments) SST = 800 (Total Sum of Squares) The number of degrees of freedom corresponding to between-treatments is

(Multiple Choice)

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Question 27

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 64 8 Within Treatments (Error) 2 TOTAL 100 The number of degrees of freedom corresponding to between-treatments is

(Multiple Choice)

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Question 28

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations).Also, the design provided the following information. SSTR $= 200$ (Sum of Squares Due to Treatments) SST $= 800$ (Total Sum of Squares) The sum of squares due to error (SSE) is

(Multiple Choice)

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Question 29

Consider the following ANOVA table. Source of Variation Sum of Squares Degrees of Freed om Mean Square F Between Treatments 2073.6 4 Between Blocks 6000 5 1200 Error 20 288 Total 29 The null hypothesis is to be tested at the 5% level of significance.The p-value is

(Multiple Choice)

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Question 30

When an analysis of variance is performed on samples drawn from k populations, the mean square due to treatments (MSTR) is

(Multiple Choice)

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Question 31

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations).Also, the design provided the following information. SSTR = 200 (Sum of Squares Due to Treatments) SST = 800 (Total Sum of Squares) If, at a 5% level of significance, we want to determine whether or not the means of the five populations are equal, the critical value of F is

(Multiple Choice)

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Question 32

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6.The MSE for this situation is

(Multiple Choice)

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Question 33

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = .01 is

(Multiple Choice)

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Question 34

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below. Treatment Observations A 20 30 25 33 B 22 26 20 28 40 30 28 22 The null hypothesis for this ANOVA problem is

(Multiple Choice)

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Question 35

Consider the following information. =6750 H0:\mu1=\mu2=\mu3=\mu4 =8000 : At least one mean is different The mean square due to treatments (MSTR) equals

(Multiple Choice)

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Question 36

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 64 8 Within Treatments (Error) 2 TOTAL 100 If we want to determine whether or not the means of the populations are equal, the p-value is

(Multiple Choice)

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Question 37

In a completely randomized design involving four treatments, the following information is provided. Treatment 1 Treatment 2 Treatment 3 Treatment 4 Sample Size 50 18 15 17 Sample Mean 32 38 42 48 The overall mean (the grand mean) for all treatments is

(Multiple Choice)

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Question 38

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 64 8 Within Treatments (Error) 2 TOTAL 100 At a 5% level of significance, if we want to determine whether or not the means of the populations are equal, the conclusion of the test is that

(Multiple Choice)

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Question 39

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 180 3 Within Treatments (Error) TOTAL 480 18 The mean square due to treatments (MSTR) is

(Multiple Choice)

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Question 40

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 64 8 Within Treatments (Error) 2 TOTAL 100 The mean square due to treatments (MSTR) is

The process of using the same or similar experimental units for all treatments is called

The required condition for using an ANOVA procedure on data from several populations is that the

Consider the following ANOVA table. Source of Variation Sum of Squares Degrees of Freed om Mean Square F Between Treatments 2073.6 4 Between Blocks 6000 5 1200 Error 20 288 Total 29 The test statistic to test the null hypothesis equals

The ANOVA procedure is a statistical approach for determining whether or not the means of

In an ANOVA procedure, a term that means the same as the term "variable" is

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 64 8 Within Treatments (Error) 2 TOTAL 100 The number of degrees of freedom corresponding to between-treatments is

Consider the following ANOVA table. Source of Variation Sum of Squares Degrees of Freed om Mean Square F Between Treatments 2073.6 4 Between Blocks 6000 5 1200 Error 20 288 Total 29 The null hypothesis is to be tested at the 5% level of significance.The p-value is

When an analysis of variance is performed on samples drawn from k populations, the mean square due to treatments (MSTR) is

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6.The MSE for this situation is

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = .01 is

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below. Treatment Observations A 20 30 25 33 B 22 26 20 28 40 30 28 22 The null hypothesis for this ANOVA problem is

Consider the following information. =6750 H0:\mu1=\mu2=\mu3=\mu4 =8000 : At least one mean is different The mean square due to treatments (MSTR) equals

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 64 8 Within Treatments (Error) 2 TOTAL 100 If we want to determine whether or not the means of the populations are equal, the p-value is

In a completely randomized design involving four treatments, the following information is provided. Treatment 1 Treatment 2 Treatment 3 Treatment 4 Sample Size 50 18 15 17 Sample Mean 32 38 42 48 The overall mean (the grand mean) for all treatments is

Part of an ANOVA table is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F Between Treatments 180 3 Within Treatments (Error) TOTAL 480 18 The mean square due to treatments (MSTR) is

Data and Statistics

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Introduction to Probability

Discrete Probability Distributions

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Inference About Means and Proportions With Two Populations

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Comparing Multiple Proportions, Test of Independence and Goodness of Fit

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