Question 1

The analysis of variance is an inferential method that is used to test the equality of

Accepted Answer

A)  three or more population means. 
B)  three or more population variances. 
C)  two population means. 
D)  two population variances.

Question 2

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 test statistic F to test the hypothesis that there is no difference in the average age of each group. Use $\alpha = 0.01$.

Accepted Answer

A)  2.517 
B)  2.913 
C)  3.189 
D)  $4.312$

Question 3

Conduct Analysis of Variance on the Randomized Complete Block Design
-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. Is there any interaction effect? Answer Yes or No. Test at $\alpha = 0.05$.
$\begin{array}{|l|c|c|c|}
\hline & \text { Cottage } & \text { Bi-Level } & 2 \text { story } \
\hline \text { Smith } & 27,34,30,35,39 & 25,47,44,30,39 & 28,24,29,32,41 \
\hline \text { Jones } & 46,41,37,26,24 & 31,39,44,45,32 & 43,45,44,36,31 \
\hline
\end{array}$

Accepted Answer

A)  No 
B)  Yes

Question 4

Conduct Analysis of Variance on the Randomized Complete Block Design
-A researcher is testing the percent weight gain on mice of varying ages based upon the diet they eat. He has 4 mice in each age category: 6 months, 9 months, 12 months and 15 months. They mice are weighed, fed only one of four diets and weighed after 1 month. The weight gain percent is then recorded. The data is given below. Test at $\alpha = 0.05$ if there is a difference in weights.
$\begin{array}{|l|c|c|c|c|}
\hline & \text { Diet A } & \text { Diet B } & \text { Diet C } & \text { Diet D } \
\hline 6 \text { months } & 5.2 & 5.3 & 5.8 & 5.6 \
\hline 9 \text { months } & 5.0 & 5.7 & 5.6 & 5.2 \
\hline 12 \text { months } & 5.3 & 6.1 & 6.1 & 5.0 \
\hline 15 \text { months } & 4.9 & 6.4 & 5.7 & 5.1 \
\hline
\end{array}$

Accepted Answer

A)  Diet does result in significantly different weight gains. 
B)  Diet does not result in significantly different weight gains.

Question 5

Perform the Tukey Test
-Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is given below. Use $\alpha = 0.01$. Which of the following is a correct statement about the means?

Accepted Answer

A)  The mean of Insecticide 1 is equal to mean of Insecticide $2 .$ 
B)  The mean of Insecticide 2 is equal to mean of Insecticide $3 .$ 
C)  The mean of Insecticide 3 is equal to mean of Insecticide 1 . 
D)  The mean of Insecticide 1 is equal to mean of Insecticide $4 .$

Question 6

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-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. Test the hypothesis that there is no difference among the means. Use $\alpha = 0.05$.

Accepted Answer

The answer of Test a Hypothesis Regarding Three or More...

Question 7

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. State the requirements that must be satisfied in order to use the one-way ANOVA procedure.

Accepted Answer

The answer of A researcher wishes to determine whether there...

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 test statistic $F$ 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)  $8.357$ 
B)  $8.123$ 
C)  $7.123$ 
D)  $6.912$

Question 9

Conduct Analysis of Variance on the Randomized Complete Block Design
-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. The facilitator is interested in determining if there is an increase in confidence the longer the managers train. Answer Yes or No. 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)  Yes 
B)  No

Question 10

Perform the Tukey Test
-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. Use $\alpha = 0.05$. Which of the following is a correct statement about the means?

Accepted Answer

A)  The mean of Group 1 is not equal to mean Group 2 . 
B)  The mean of Group 1 is not equal to mean Group $3 .$ 
C)  The mean of Group 2 is not equal to mean Group $3 .$ 
D)  All of the means are not equal.

Question 11

Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is recorded. State the requirements that must be satisfied in order to use the one-way ANOVA procedure.

Accepted Answer

The answer of Four different types of insecticides are used...

Question 12

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-$\text { Test the hypothesis that the populations have the same mean. Use } \alpha=0.05 \text {. }$

Accepted Answer

The answer of Test a Hypothesis Regarding Three or More...

Question 13

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-Which of the following is not an example of a mean square?

Accepted Answer

A)  $\mu ^ { 2 }$ 
B)  $\frac { n _ { 1 } ( \bar { x } 1 - \bar { x } ) + n _ { 2 } ( \bar { x } 2 - \bar { x } ) + \ldots + n _ { k } ( \bar { x } k - \bar { x } ) } { k - 1 }$ 
C)  $\sigma ^ { 2 }$ 
D)  $\frac { \left( \mathrm { n } _ { 1 } - 1 \right) \mathrm { s } _ { 1 } ^ { 2 } + \left( \mathrm { n } _ { 2 } - 1 \right) \mathrm { s } _ { 2 } ^ { 2 } + \ldots + \left( \mathrm { n } _ { \mathrm { k } } - 1 \right) \mathrm { s } _ { \mathrm { k } } ^ { 2 } } { \mathrm { n } - \mathrm { k } }$

Question 14

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 19 physicians from each of the three certification levels-- Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per-member, per-month charges for each (a total of 19 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance.
Write the null hypothesis tested by the ANOVA.

Accepted Answer

A)  $\mathrm { H } _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } }$ 
B)  $\mathrm { H } _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$ 
C)  $\mathrm { H } _ { 0 } : \mu _ { \mathrm { C } } = \mu _ { \mathrm { E } } = \mu _ { \mathrm { I } } = 0$ 
D)  $\mathrm { H } _ { 0 } : \mathrm { p } 1 = \mathrm { p } 2 = \mathrm { p } 3$

Question 15

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that Certification Level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 20 physicians from each of the three certification levels -- Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-- and recorded the total per member per month charges for each (a total of 60 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. The results of the ANOVA are summarized in the following table. Take $\alpha = 0.01$. Interpret the $\mathrm { P }$-value of the ANOVA F test.

Accepted Answer

A)  The means of the total per member per month charges for the three groups of physicians differ at $\alpha = 0.01$. 
B)  The model is not statistically useful (at $\alpha = 0.01$ ) for prediction purposes. 
C)  The variances of the total per number per month charges for the three groups of physicians differ at $\alpha = 0.01 .$ 
D)  The means of the total per member per month charges for the three groups of physicians are equal at $\alpha = 0.01$.

Question 16

Perform the Tukey Test
-The grade point averages of students participating in sports at a local community college are to be compared. The data are listed below. Which of the following is a correct statement about the means? Use $\alpha = 0.05$.

Accepted Answer

A)  The mean grade point average of hockey players is the same as the mean grade point average of basketball players. 
B)  The mean grade point average of hockey players is the same as the mean grade point average of track participants. 
C)  The mean grade point average of basketball players is the same as the mean grade point average of track participants. 
D)  The mean grade point average of each sport is the same.

Question 17

Perform the Tukey Test
-A cell phone company is investigating whether age and ethnicity are factors which explain how much people spend on their cell phones. They randomly picked three people from each category and determined each person's average monthly cell phone bill. The results are shown in the table. Amounts are in dollars. 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 the three age groups, use Tukey's test to determine which pairwise means differ using a familywise error rate of $\alpha = 0.05$. Give the P-value for any significant differences. If there is a significant difference in the means for the three ethnic groups, 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.

Accepted Answer

The answer of Perform the Tukey Test
-A cell phone company...

Question 18

Conduct Analysis of Variance on the Randomized Complete Block Design
-Why is the completely randomized block design not always sufficient

Accepted Answer

The answer of Conduct Analysis of Variance on the Randomized...

Question 19

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. At $\alpha = 0.05$, what would be the best interpretation?

Accepted Answer

A)  At $\alpha = 0.05$, it can be said that color doesn't matter 
B)  At $\alpha = 0.05$, light green has a higher mean than gray 
C)  At $\alpha = 0.05$, it can be said that at least one color has a different mean 
D)  At $\alpha = 0.05$, red is the best color

Question 20

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA
-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. Find the test statistic $F$ to test the hypothesis that there is no difference among the means. Use $\alpha = 0.05$.

Accepted Answer

A)  $11.095$ 
B)  $9.812$ 
C)  $8.369$ 
D)  $12.162$

Exam 13: Comparing Three or More Means

The analysis of variance is an inferential method that is used to test the equality of

Perform the Tukey Test -Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is given below. Use α=0.01\alpha = 0.01α=0.01 . Which of the following is a correct statement about the means?

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. State the requirements that must be satisfied in order to use the one-way ANOVA procedure.

Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is recorded. State the requirements that must be satisfied in order to use the one-way ANOVA procedure.

Test a Hypothesis Regarding Three or More Means Using One -Way ANOVA -Which of the following is not an example of a mean square?

Perform the Tukey Test -The grade point averages of students participating in sports at a local community college are to be compared. The data are listed below. Which of the following is a correct statement about the means? Use α=0.05\alpha = 0.05α=0.05 .

Conduct Analysis of Variance on the Randomized Complete Block Design -Why is the completely randomized block design not always sufficient