Question 1

Conduct Analysis of Variance on the Randomized Complete Block Design
-True or False: It is required for the Two-Way ANOVA that the samples be dependent.

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True A

Question 2

Conduct Analysis of Variance on the Randomized Complete Block Design
-A farmer has a 160 acre tract of land that he is planting in corn. He has heard about advances in fertilizer technology that impacts yield. He divides his field into four sections and each section into four parts. He has three type of fertilizer to test and no fertilizer. He randomly selects a part of a section and then randomly selects a type of fertilizer for that part of a section so that each section has all four applications applied to it. The yields in bushel per acres are given below. Test at $\alpha = 0.05$ if there is a difference in yields.
$\begin{array}{|l|c|c|c|c|}
\hline & \text { Field A } & \text { Field B } & \text { Field C } & \text { Field D } \
\hline \text { No fertilizer } & 5.7 & 10.4 & 7.3 & 9.0 \
\hline \text { Traditional } & 4.5 & 8.6 & 6.1 & 10.6 \
\hline \text { Liquid } & 4.1 & 6.3 & 5.8 & 7.2 \
\hline \text { Granular } & 2.6 & 7.2 & 4.6 & 8.7 \
\hline
\end{array}$

Accepted Answer

A)  Fertilizer does result in significantly different yields. 
B)  Fertilizer does not result in significantly different yields. 
A)  Fertilizer does result in significantly different yields. 
B)  Fertilizer does not result in significantly different yields. A

Question 3

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" - five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60 -pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance. Give the null hypothesis for the ANOVA F test shown on the printout.

Accepted Answer

A)  $\mathrm { H } _ { 0 } : \mu _ { \mathrm { green } } = \mu _ { \mathrm { blue } } = \mu _ { \mathrm { gray } } = \mu _ { \mathrm { red } }$, where the $\mu _ { \text {'s represent mean attitudes for the four rooms } }$ 
B)  $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 } = \mu _ { 5 }$, where the $\mu _ { \mathrm { i } }$ represent attitude means for the ith person in each room 
C)  $\mathrm { H } _ { 0 } : \mathrm { x } _ { 1 } = \mathrm { x } _ { 2 } = \mathrm { x } _ { 3 } = \mathrm { x } _ { 4 }$, where the $\mathrm { x } ^ { \prime }$ s represent the room colors 
D)  $\mathrm { H } _ { 0 } :$ Pgreen $^ { \text {g } }$ Pblue $=$ pgray $^ { \text {gre } }$ pred, where the p's represent the proportion with the corresponding attitude 
A)  $\mathrm { H } _ { 0 } : \mu _ { \mathrm { green } } = \mu _ { \mathrm { blue } } = \mu _ { \mathrm { gray } } = \mu _ { \mathrm { red } }$, where the $\mu _ { \text {'s represent mean attitudes for the four rooms } }$ 
B)  $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 } = \mu _ { 5 }$, where the $\mu _ { \mathrm { i } }$ represent attitude means for the ith person in each room 
C)  $\mathrm { H } _ { 0 } : \mathrm { x } _ { 1 } = \mathrm { x } _ { 2 } = \mathrm { x } _ { 3 } = \mathrm { x } _ { 4 }$, where the $\mathrm { x } ^ { \prime }$ s represent the room colors 
D)  $\mathrm { H } _ { 0 } :$ Pgreen $^ { \text {g } }$ Pblue $=$ pgray $^ { \text {gre } }$ pred, where the p's represent the proportion with the corresponding attitude A

Question 4

Conduct Analysis of Variance on the Randomized Complete Block Design
-True or False: In the completely randomized block design, a single factor is manipulated and fixed at different levels.

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 5

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-The grade point averages of students participating in sports at a local college are to be compared. The data are listed below. Test the hypothesis that there is no difference in the mean grade point averages of the 3 groups. Use $\alpha = 0.05$.

Accepted Answer

critical valueF @#LAT-DLM&; test statist

Question 6

Draw Interaction Plots
-A builder has two crews that construct homes. He is interested in determining if there is a difference in the time it takes the crews to build three different styles of homes. The time in days for each crew is given below. What type of interaction is revealed by the interaction plot? Test at $\alpha = 0.05$.
$\begin{array}{|l|c|c|c|}
\hline & \text { Cottage } & \text { Bi-Level } & \text { 2 story } \
\hline \text { Smith } & 27,34,30,35,39 & 25,47,44,30,39 & 28,24,29,32,41 \
\hline \text { Jones } & 46,41,37,26,24 & 31,39,44,45,32 & 43,45,44,36,31 \
\hline
\end{array}$

Accepted Answer

A)  No interaction 
B)  Significant interaction 
C)  Some interaction 
D)  Complete interaction 
A)  No interaction 
B)  Significant interaction 
C)  Some interaction 
D)  Complete interaction

Question 7

Draw Interaction Plots
-A training program is supposed to develop self confidence in managers. The two-week program is administered to six males and six females. All participants are tested after the end of the first week and after the end of the second week. The scores of those tests are given below. What type of interaction is revealed by the interaction plot? Test at $\alpha = 0.05$.
$\begin{array}{|l|c|c|}
\hline & \text { Week One } & \text { Week Two } \
\hline \text { Men } & 65,81,81,75,88,75 & 90,94,80,91,81,98 \
\hline \text { Women } & 71,76,82,88,87,75 & 81,97,86,91,99,83 \
\hline
\end{array}$

Accepted Answer

A)  No interaction 
B)  Significant interaction 
C)  Some interaction 
D)  Complete interaction 
A)  No interaction 
B)  Significant interaction 
C)  Some interaction 
D)  Complete interaction

Question 8

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is given below. Find the critical value $\mathrm { F }$-value to test the hypothesis that the type of insecticide makes no difference in the mean number of strawberries per plant. Use $\alpha = 0.01$.

Accepted Answer

A)  $4.94$ 
B)  $4.43$ 
C)  $26.69$ 
D)  $4.18$ 
A)  $4.94$ 
B)  $4.43$ 
C)  $26.69$ 
D)  $4.18$

Question 9

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-The times (in minutes) to assemble a component for 3 different cell phones are listed below. Workers are randomly selected. Test the hypothesis that there is no difference in the mean time for each cell phone. Use $\alpha =$ $0.01$.

Accepted Answer

critical value @#LAT-DLM&; test statisti

Question 10

A medical researcher wishes to try three different techniques to lower cholesterol levels of patients with high cholesterol levels. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subject s cholesterol level is recorded. State the requirements that must be satisfied in order to use the one-way ANOVA procedure.

Accepted Answer

Each group represents a simple random sa

Question 11

Conduct Analysis of Variance on the Randomized Complete Block Design
-To conduct an analysis of variance on a randomized complete block design a researcher would use

Accepted Answer

A)  a two-way ANOVA. 
B)  a one-way ANOVA. 
C)  a Tukey Test. 
D)  a Scheffe' Test. 
A)  a two-way ANOVA. 
B)  a one-way ANOVA. 
C)  a Tukey Test. 
D)  a Scheffe' Test.

Question 12

Conduct Analysis of Variance on the Randomized Complete Block Design
-True or False: It is required for the Two-Way ANOVA that the populations from which the samples are drawn are normal.

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 13

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is given below. Test the hypothesis that the type of insecticide makes no difference in the mean number of strawberries per plant. Use $\alpha = 0.01$.

Accepted Answer

critical value F0.01,3,20 = 4.

Question 14

Perform the Tukey Test
-A two-way analysis of variance is to be performed using the data below. Assume that the data come from populations that are normally distributed with the same variance. If there is a significant difference in the means for the three levels of factor A, use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$. If there is a significant difference in the means for the three levels of factor B, use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$.

Accepted Answer

Among levels of factor A:
Tukey's test i

Question 15

How, in general, is the requirement of equal population variances to allow the use of analysis of variance method verified

Accepted Answer

A)  The largest sample standard deviation must be less than or equal to twice the smallest sample standard deviation. 
B)  All three sample standard deviations must be equal. 
C)  The largest sample standard deviation is equal to the sum of the other standard deviations. 
D)  The largest sample standard deviation is less than or equal to the variance of the smallest sample. 
A)  The largest sample standard deviation must be less than or equal to twice the smallest sample standard deviation. 
B)  All three sample standard deviations must be equal. 
C)  The largest sample standard deviation is equal to the sum of the other standard deviations. 
D)  The largest sample standard deviation is less than or equal to the variance of the smallest sample.

Question 16

Perform the Tukey Test
-The times (in minutes) to assemble a component for three different cell phones are listed below. Use $\alpha = 0.01$. Which of the following is correct?

Accepted Answer

A)  The mean time to assemble Phone 1 is the same as the mean time to assemble Phone $2 .$ 
B)  The mean time to assemble Phone 1 is different from the mean time to assemble Phone $3 .$ 
C)  The mean time to assemble Phone 2 is the same as the mean time to assemble Phone 3 . 
D)  There is not enough evidence to suggest that the means are different. 
A)  The mean time to assemble Phone 1 is the same as the mean time to assemble Phone $2 .$ 
B)  The mean time to assemble Phone 1 is different from the mean time to assemble Phone $3 .$ 
C)  The mean time to assemble Phone 2 is the same as the mean time to assemble Phone 3 . 
D)  There is not enough evidence to suggest that the means are different.

Question 17

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-A researcher wishes to determine whether there is a difference in the average age of middle school, high school, and college teachers. Teachers are randomly selected. Their ages are recorded below. Find the critical value F-value to test the hypothesis that there is no difference in the average age of each group. Use $\alpha = 0.01$.

Accepted Answer

A)  6.363 
B)  5.09 
C)  9.43 
D)  $5.42$ 
A)  6.363 
B)  5.09 
C)  9.43 
D)  $5.42$

Question 18

Perform the Tukey Test
-A researcher is investigating whether gender and exercise are factors which explain resting pulse rate in her adult patients. She randomly selected three patients from each category and recorded their resting pulse rates. The results are given in the table. Pulse rates are in beats per minute. A two-way analysis of variance is to be performed. Assume that the data come from populations that are normally distributed with the same variance. If there is a significant difference in the means for gender, use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$. Give the $\mathrm { P }$-value for any significant differences. If there is a significant difference in the means for the three exercise levels, use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$. Give the $\mathrm { P }$-value for any significant differences.
 
Levels of the factor exercise are defined as follows:
level 1: little or no exercise.
level 2: regular moderate exercise
level 3: regular vigorous exercise

Accepted Answer

Gender:
Tukey's test indicates that the

Question 19

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-Find the test statistic F to test the hypothesis that the populations have the same mean. Use $\alpha = 0.05$.

Accepted Answer

A)  $1.403 $ 
B)  $1.021$ 
C)  $1.182$ 
D)  $0.832$ 
A)  $1.403 $ 
B)  $1.021$ 
C)  $1.182$ 
D)  $0.832$

Question 20

Conduct Analysis of Variance on the Randomized Complete Block Design
-Assume that the data below come from populations that are normally distributed with the same variance. Let $\mu _ { 1 }$ be the mean for treatment $1 , \mu _ { 2 }$ the mean for treatment 2 , and $\mu _ { 3 }$ the mean for treatment 3 . In a test of $\mathrm { H } _ { 0 }$ : $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ versus $\mathrm { H } _ { 1 }$ : at least one of the means is different, the null hypothesis is rejected at the $\alpha = 0.05$ level of significance. Use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$. Give the $\mathrm { P }$-value for each of the pairwise tests and state your conclusion.

Accepted Answer

\[\begin{array} { l } 
\mathrm { H } _ {

Conduct Analysis of Variance on the Randomized Complete Block Design -True or False: It is required for the Two-Way ANOVA that the samples be dependent.

Conduct Analysis of Variance on the Randomized Complete Block Design -True or False: In the completely randomized block design, a single factor is manipulated and fixed at different levels.

Conduct Analysis of Variance on the Randomized Complete Block Design -To conduct an analysis of variance on a randomized complete block design a researcher would use

Conduct Analysis of Variance on the Randomized Complete Block Design -True or False: It is required for the Two-Way ANOVA that the populations from which the samples are drawn are normal.

How, in general, is the requirement of equal population variances to allow the use of analysis of variance method verified

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Exam 13: Comparing Three or More Means

Conduct Analysis of Variance on the Randomized Complete Block Design -True or False: It is required for the Two-Way ANOVA that the samples be dependent.

Conduct Analysis of Variance on the Randomized Complete Block Design -True or False: In the completely randomized block design, a single factor is manipulated and fixed at different levels.

Conduct Analysis of Variance on the Randomized Complete Block Design -To conduct an analysis of variance on a randomized complete block design a researcher would use

Conduct Analysis of Variance on the Randomized Complete Block Design -True or False: It is required for the Two-Way ANOVA that the populations from which the samples are drawn are normal.

How, in general, is the requirement of equal population variances to allow the use of analysis of variance method verified

Perform the Tukey Test -The times (in minutes) to assemble a component for three different cell phones are listed below. Use α=0.01\alpha = 0.01α=0.01 . Which of the following is correct?

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA -Find the test statistic F to test the hypothesis that the populations have the same mean. Use α=0.05\alpha = 0.05α=0.05 .

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters