Question 1

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

Accepted Answer

A)  133.2 
B)  13.32 
C)  14.8 
D)  30.0 
A)  133.2 
B)  13.32 
C)  14.8 
D)  30.0 C

Question 2

Random samples of individuals from three different cities were asked how much time they spend per day watching television. The results (in minutes) for the three groups are shown below. $$\begin{array} { c c c } 
\text { City I } & \text { City II } & \text { City III } \
260 & 178 & 211 \
280 & 190 & 190 \
240 & 220 & 250 \
260 & 240 & \
300 & &
\end{array}$$ At α = .05, use Excel to test to see if there is a significant difference in the averages of the three groups.

Accepted Answer

\(\begin{array}{|l|l|l|l|l|l|l|l|} \hline & \text { A } & \text { B } & \text { C } & \text { D }& \text { E } & \text { F } & \text { G } \ \hline \mathbf{1} & \text { Observation } & \text { City I } & \text { City II } & \text { City III } \ \hline 2 & 1 & 260 & 178 & 211 \ \hline 3 & 2 & 280 & 190 & 190 \ \hline 4 & 3 & 240 & 220 & 250 \ \hline 5 & 4 & 260 & 240 & \ \hline 6 & 5 & 300 & &\\hline 7 & \ \hline 8 & \text { Anova: Single Fac tor } \ \hline 9 & \ \hline 10 & \text { SUMMARY } \\hline \mathbf{1 1} & \text { Groups } & \text { Count } & \text { Sum } & \text { Average } & \text { Variance } \ \hline \mathbf{1 2} & \text { City I } & 5 & 1340 & 268 & 520 \ \hline \mathbf{1 3} & \text { City II } & 4 & 828 & 207 & 796 \ \hline \mathbf{1 4} & \text { City III } & 3 & 651 & 217 & 927 \\hline15 & \ \hline 16 & \text { ANOVA }\ \hline 17 & \text { Source of Variation } & S S & d f & M S & F & \text { P-value } & F_{\text {crit }} \ \hline 18 & \text { Between Groups } & 9552.92 & 2 & 4776.458 & 6.79977 & 0.01587 & 4.25649 \ \hline 19 & \text { Within Groups } & 6322.00 & 9 & 702.444 & & & \\hline 20 & & & \ \hline 21 & \text { Total } & 15874.92 & 11 \\hline \end{array}\) Reject H_0, conclude that there is a significant difference in the averages of the three groups

Question 3

Individuals were randomly assigned to three different production processes. The hourly units of production for the three processes are shown below. $$\begin{array}{l}
\text { Production Process }\
\begin{array} { c c c } 
\text { Process 1 } & \text { Process 2 } & \text { Process 3 } \
33 & 33 & 28 \
30 & 35 & 36 \
28 & 30 & 30 \
29 & 38 & 34
\end{array}
\end{array}$$ Use Excel with α = .05 to determine whether there is a significant difference in the mean hourly units of production for the three types of production processes.

Accepted Answer

​ \(\begin{array}{|l|l|l|l|l|l|l|l|}
\hline & \text { A } & \text { B } & \text { C } & \text { D }& \text { E }& \text { F }& \text { G } \
\hline \mathbf{1} & \text { Observation } & \text { Process 1 } & \text { Process 2 } & \text { Process 3 } \
\hline \mathbf{2} & 1 & 33 & 33 & 28 \
\hline \mathbf{3} & 2 & 30 & 35 & 36 \
\hline \mathbf{4} & 3 & 28 & 30 & 30 \
\hline \mathbf{5} & 4 & 29 & 38 & 34 \
\hline \mathbf{6} & & & & \
\hline 7 & \text { Anova: SingleF actor } & & & \\hline 8 & \
\hline 9 & \text { SLMMARY } \\hline10 & \text { Groups } & \text { Count } & \text { Sum } & \text { Average } & \text { Voriance } \
\hline \mathbf{1 1} & \text { Process 1 } & 4 & 120 & 30 & 4.66667 \
\hline \mathbf{1 2} & \text { Process 2 } & 4 & 136 & 34 & 11.33333 \
\hline \mathbf{1 3} & \text { Process 3 } & 4 & 128 & 32 & 13.33333\\hline 14 & \
\hline 15 & \mathrm{ANOVA} \\hline \mathbf{1 6} & \text { Source ofVoriation } & S S & d f & M S & F & \text { P-value } & \text { F crit } \
\hline \mathbf{1 7} & \text { Between Groups } & 32 & 2 & 16.00000 & 1.63636 & 0.24766 & 4.25649 \
\hline \mathbf{1 8} & \text { Within Groups } & 88 & 9 & 9.77778 & & & \\hline 19 & & & \
\hline 20 & \text { Total } & 120 & 11 \
\hline
\end{array}\) We cannot conclude that there is a significant difference in the mean hourly units of production for the three types of production processes.

Question 4

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

Accepted Answer

A)  40.0 
B)  37.3 
C)  48.0 
D)  37.0 
E)  None of the answers is correct. 
A)  40.0 
B)  37.3 
C)  48.0 
D)  37.0 
E)  None of the answers is correct.

Question 5

Three different models of automobiles (A, B, and C) were compared for gasoline consumption. For each model of car, fifteen cars were randomly selected and subjected to standard driving procedures. The average miles/gallon obtained for each model of car and sample standard deviations are shown below. $$\begin{array}{l}
&\text { Car } A & \text { Car B } & \text { Car C } \
\text { Average miles per gallon }&42 & 49 & 44 \
\text { Sample standard deviation }&4 & 5 & 3
\end{array}$$ Use the above data and test to see if the mean gasoline consumption for all three models of cars is the same. Let α = .05.
​

Accepted Answer

@#IMG-DLM& F = 11.7 > 3.21; reject H_0, c

Question 6

In ANOVA, which of the following is NOT affected by whether or not the population means are equal?

Accepted Answer

A)  $\bar{x}$ 
B)  between-samples estimate of $\sigma$ 2  
C)  within-samples estimate of $\sigma$ 2 
D)  None of the answers is correct. 
A)  $\bar{x}$ 
B)  between-samples estimate of $\sigma$ 2  
C)  within-samples estimate of $\sigma$ 2 
D)  None of the answers is correct.

Question 7

Three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds of the tested cars are given below. $$\begin{array} { c c c } 
\text { Manufacturer A } & \text { Manufacturer B } & \text { Manufacturer C } \
\hline 180 & 177 & 175 \
175 & 180 & 176 \
179 & 167 & 177 \
176 & 172 & \
190 & &
\end{array}$$ At α = .05, use Excel to determine whether there is a significant difference in the average speeds of the cars of the auto manufacturers.

Accepted Answer

@#IMG-DLM& Do not reject H_0, cannot conc

Question 8

Random samples were selected from three populations. The data obtained are shown below. $$\begin{array} { c c c } 
\text { Treatment 1 } & \text { Treatment 2 } & \text { Treatment 3 } \
45 & 30 & 39 \
41 & 34 & 35 \
37 & 35 & 38 \
40 & 40 &
\end{array}$$ At a 5% level of significance, test to see if there is a significant difference in the means of the three populations. (Please note that the sample sizes are not equal.)
​

Accepted Answer

Since the test statistic F = 4

Question 9

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is _____.

Accepted Answer

A)  SSE/(nT - k) 
B)  SSTR/(nT - k) 
C)  SSE/(k - 1) 
D)  SSE/k 
A)  SSE/(nT - k) 
B)  SSTR/(nT - k) 
C)  SSE/(k - 1) 
D)  SSE/k

Question 10

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

Accepted Answer

A)  40.0 
B)  37.3 
C)  48.0 
D)  37.0 
E)  None of the answers is correct. 
A)  40.0 
B)  37.3 
C)  48.0 
D)  37.0 
E)  None of the answers is correct.

Question 11

For four populations, the population variances are assumed to be equal. Random samples from each population provide the following data. $$\begin{array} { c c c c } 
\text { Population } & \text { Sample Size } & \text { Sample Mean } & \text { Sample Variance } \
1 & 11 & 40 & 23.4 \
2 & 11 & 35 & 21.6 \
3 & 11 & 39 & 25.2 \
4 & 11 & 37 & 24.6
\end{array}$$ Using a .05 level of significance, test to see if the means for all four populations are the same.

Accepted Answer

Do not reject the nu

Question 12

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

Accepted Answer

A)  factor block design 
B)  random factor design 
C)  completely randomized design 
D)  None of the answers is correct. 
A)  factor block design 
B)  random factor design 
C)  completely randomized design 
D)  None of the answers is correct.

Question 13

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

Accepted Answer

A)  3.74 
B)  2.25 
C)  2.37 
D)  1.96 
A)  3.74 
B)  2.25 
C)  2.37 
D)  1.96

Question 14

The final examination grades of random samples of students from three different classes are shown below. $$\begin{array} { c c c } 
\text { Class A } & \text { Class B } & \text { Class C } \
92 & 91 & 85 \
85 & 85 & 93 \
96 & 90 & 82 \
95 & 86 & 84
\end{array}$$ At the α = .05 level of significance, is there any difference in the mean grades of the three classes?

Accepted Answer

MSTR = 37.34
MSE = 18.89
F = 1

Question 15

In a completely randomized experimental design, 11 experimental units were used for each of the four treatments. Part of the ANOVA table is shown below. $\begin{array}{lllll}
\text { Source of Variation } & \text { Sum of } & \text { Degrees of } & \text { Mean } & F \
& \text { Squares } & \text { Freedom } & \text { Square } &\
\hline \text {Between treatments }&1,500&\_\_\_\_?&\_\_\_\_?&\_\_\_\_?\
 \text {  Within treatments (Error)}&\_\_\_\_?&\_\_\_\_?&\_\_\_\_?\
\hline \text { Total}&5,500\
\end{array}$ Fill in the blanks in the above ANOVA table.
​

Accepted Answer

The answer of In a completely randomized experimental design, 11...

Question 16

An experimental design that permits statistical conclusions about two or more factors is a _____.

Accepted Answer

A)  randomized block design 
B)  factorial design 
C)  completely randomized design 
D)  randomized design 
A)  randomized block design 
B)  factorial design 
C)  completely randomized design 
D)  randomized design

Question 17

In the ANOVA, treatment refers to _____.

Accepted Answer

A)  experimental units 
B)  different levels of a factor 
C)  a factor 
D)  applying antibiotic to a wound 
A)  experimental units 
B)  different levels of a factor 
C)  a factor 
D)  applying antibiotic to a wound

Question 18

In the analysis of variance procedure (ANOVA), factor refers to _____.

Accepted Answer

A)  the dependent variable 
B)  the independent variable 
C)  different levels of a treatment 
D)  the critical value of F 
A)  the dependent variable 
B)  the independent variable 
C)  different levels of a treatment 
D)  the critical value of F

Question 19

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

Accepted Answer

A)  factor block design 
B)  random factor design 
C)  completely randomized design 
D)  None of the answers is correct. 
A)  factor block design 
B)  random factor design 
C)  completely randomized design 
D)  None of the answers is correct.

Question 20

Five drivers were selected to test drive two makes of automobiles. The following table shows the number of miles per gallon for each driver driving each car. $\begin{array}{llllll}
&&&\text { Driver }\
\text { Automobile }&1&2&3&4&5\
A & 30 & 31 & 30 & 27 & 32 \
B & 36 & 35 & 28 & 31 & 30
\end{array}$ Consider the makes of automobiles as treatments and the drivers as blocks and use Excel to determine whether there is any difference in the miles/gallon of the two makes of automobiles. Let α = .05.

Accepted Answer

​ @#IMG-DLM& We cannot conclude that the

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

In ANOVA, which of the following is NOT affected by whether or not the population means are equal?

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments 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 _____.

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

The final examination grades of random samples of students from three different classes are shown below. Class A Class B Class C 92 91 85 85 85 93 96 90 82 95 86 84 At the α = .05 level of significance, is there any difference in the mean grades of the three classes?

An experimental design that permits statistical conclusions about two or more factors is a _____.

In the ANOVA, treatment refers to _____.

In the analysis of variance procedure (ANOVA), factor refers to _____.

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence, and Multiple Proportions

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

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Exam 13: Experimental Design and Analysis of Variance

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

In ANOVA, which of the following is NOT affected by whether or not the population means are equal?

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments 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 _____.

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

The final examination grades of random samples of students from three different classes are shown below. Class A Class B Class C 92 91 85 85 85 93 96 90 82 95 86 84 At the α = .05 level of significance, is there any difference in the mean grades of the three classes?

An experimental design that permits statistical conclusions about two or more factors is a _____.

In the ANOVA, treatment refers to _____.

In the analysis of variance procedure (ANOVA), factor refers to _____.

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence, and Multiple Proportions

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters