Deck 16: Analysis of Variance Anova

Question 1

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach.
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the three different brands? The sample
data are given below.

Answer 1

Question 2

Use Minitab to perform a Kruskal-Wallis test using the P-value approach.
The table below shows the weights (in pounds)of 6 randomly selected women in each of
three different age groups. At the 0.01 significance level, do the data provide sufficient
evidence to conclude that a difference exists between the three population means?

Answer 2

Question 3

Provide an appropriate response.
A one-way ANOVA is to be performed. Independent random samples are taken from two
populations. The sample data are depicted in the dotplot below. Is it reasonable to
conclude that the difference between the sample means is due to a difference between the
population means and not to variation within the populations? Do you think the null
hypothesis would be rejected? Explain your thinking.

Answer 3

Since the variation between the sample means is large relative to the variation
within the samples, it is reasonable to conclude that the difference between the
sample means is due to a difference between the population means and not to
variation within the populations. The null hypothesis would be rejected.

Question 4

Conduct a Tukey multiple comparison. Display the confidence intervals in a table. State which population means can bedeclared different.
Perform a Tukey multiple comparison to compare the breaking strengths of four different
kinds of thread. Use a 95% family confidence level. Independent random samples of the
four different kinds of thread yielded the following breaking strengths in ounces.

Question 5

Provide an ap propriate response.
For an F-curve with df = (10, 20), find the F-value having area 0.01 to its right and
illustrate your answer with a sketch.

Question 6

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach.
The data below represent the weight losses for people on three different exercise programs. At the 1% significance level, does it appear that a difference exists in the true mean weight
loss produced by the three exercise programs?

Question 7

Perform a Kruskal-Wallis test using the critical-value approach.
A medical researcher wishes to try three different techniques to lower blood pressure of
patients with high blood pressure. 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, the reduction in each subject's
blood pressure is recorded. Use the Kruskal-Wallis test to test the claim that there is no
difference in the distribution of the populations. Us

Question 8

Conduct a Tukey multiple comparison. Display the confidence intervals in a table. State which population means can bedeclared different.
Use a 95% family confidence level.

Question 9

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach.
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the four different brands? The sample
data are given below.

Question 10

Provide an ap propriate response.
For an F-curve with df = (8, 3), find the F-value having area 0.05 to its right and illustrate
your answer with a sketch.

Question 11

Construct a normal probability plot of the given data.
The time (in minutes)it takes to assemble a computer component for 3 different machines
is listed below. Workers are randomly selected. Use the Kruskal-Wallis test to test the
claim that there is no difference in the distribution of the population

Question 12

Perform a Kruskal-Wallis test using the critical-value approach.
The table below shows the lifetimes (in hours)of random samples of light bulbs of three
different brands. At the 0.01 significance level, do the data provide sufficient evidence to
conclude that a difference exists between the three population means?

Question 13

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
Four different types of fertilizers are used on raspberry plants. The number of raspberries
on each randomly selected plant is given below. Test the claim that the type of fertilizer
makes no difference in the mean number of raspberries per plant.

Question 14

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach.
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the four different brands? The sample
data are given below.

Question 15

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
A consumer magazine wants to compare the lifetimes of ballpoint pens of three different
types. The magazine takes a random sample of pens of each type in the following table. Do the data indicate that there is a difference in mean lifetime for the three brands of
ballpoint pens? Us

Question 16

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
A realtor wishes to compare the square footage of houses in 4 different cities, all of which
are priced approximately the same. The data are listed below. Can the realtor conclude that
the mean square footage in the four cities are equa

Question 17

Conduct a Tukey multiple comparison. Display the confidence intervals in a table. State which population means can bedeclared different.
Perform a Tukey multiple comparison to compare the SAT math scores of students at three
different schools. Use a 99% family confidence level. Independent random samples of
students from the three different schools yielded the following SAT math scores.

Question 18

Use Minitab to perform a Kruskal-Wallis test using the P-value approach.
SAT scores for students selected randomly from three different schools are shown below.
At the 0.05 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the three population means?

Question 19

In the context of a one-way ANOVA, explain what is meant by variation between samples
and variation within samples.

Question 20

Perform a Kruskal-Wallis test using the critical-value approach.
The table below shows the weights (in pounds)of 6 randomly selected women in each of
three different age groups. At the 0.01 significance level, do the data provide sufficient
evidence to conclude that a difference exists between the three population means?

Question 21

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
At the 0.01 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the three different brands ? The sample
data are given below.

Question 22

Use Minitab to perform a Kruskal-Wallis test using the P-value approach.
The table below shows the lifetimes (in hours)of random samples of light bulbs of three
different brands. At the 0.01 significance level, do the data provide sufficient evidence to
conclude that a difference exists between the three population means?

Question 23

Perform a Kruskal-Wallis test using the critical-value approach.
A realtor wishes to compare the square footage of houses in 4 different cities, all of which
are priced approximately the same. The data are listed below. Use the Kruskal-Wallis test
to test the claim that there is no difference in the distribution of the populations 0.05.

Question 24

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
A medical researcher wishes to try three different techniques to lower blood pressure of
patients with high blood pressure. 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 blood pressure
is recorded. Test the claim that there is no difference among the means.

Question 25

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the four different brands? The sample
data are given below.

Question 26

Provide an appropriate response.
When performing a one-way ANOVA, two of the assumptions required are that the
populations be normally distributed and that the populations have equal standard
deviations. What rule of thumb can be used to assess the equal-standard deviations
assumption? What other method can be used to assess the normality and equal-standard
deviations assumptions?

Question 27

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the four different brands? The sample
data are given below.

Question 28

Provide an appropriate response.
A one-way ANOVA is to be performed. Independent random samples are taken from two
populations. The sample data are depicted in the dotplot below. Is it reasonable to
conclude that the difference between the sample means is due to a difference between the
population means and not to variation within the populations? Do you think the null
hypothesis would be rejected? Explain your thinking.

Question 29

Perform a Kruskal-Wallis test using the critical-value approach.
Listed below are grade averages for randomly selected students with three different
categories of high-school background. At the 0.05 significance level, do the data provide
sufficient evidence to conclude that a difference exists in the three population means?

Question 30

Provide an appropriate response.
A Tukey multiple comparison is being performed to compare the means of three
populations. If the family confidence level is 95%, of what can we be 95% confident?

Question 31

Provide an appropriate response.
Do you think that the Kruskal-Wallis test is likely to be sensitive to extreme
values/outliers? Why or why not?

Question 32

Conduct a Tukey multiple comparison. Display the confidence intervals in a table. State which population means can bedeclared different.
Use a 95% family confidence level.

Question 33

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
Random samples of four different models of cars were selected and the gas mileage of each
car was measured. The results are shown below. Test the claim that the four different models have the same population mean. Use a
significance level of 0.05.

Question 34

When performing a Tukey multiple comparison, the population means are compared
pairwise. How do you decide whether to declare two population means different? Why does this make sense?

Question 35

Use Minitab to perform a Kruskal-Wallis test using the P-value approach.
Listed below are grade averages for randomly selected students with three different
categories of high-school background. At the 0.05 significance level, do the data provide
sufficient evidence to conclude that a difference exists in the three population means?

Question 36

Provide an appropriate response.
A researcher wants to perform either a Kruskal-Wallis test or a one-way ANOVA to
compare four population means. Independent samples of sizes 7, 6, 10, and 8 are selected
from the four populations. The variable under consideration is normally distributed on
each of the four populations and the population standard deviations are equal. Are the
assumptions for the one-way ANOVA met? Are the assumptions for the Kruskal-Wallis
test met? Which test is preferable? Why?

Question 37

Perform a Kruskal-Wallis test using the critical-value approach.
SAT scores for students selected randomly from three different schools are shown below.
At the 0.05 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the three population means?

Question 38

Provide an appropriate response.
Explain the rationale behind the Kruskal-Wallis test. Explain, in particular, why a large
value of the test statistic suggests that the population means are not equal.

Question 39

Provide an appropriate response.
A one-way ANOVA is being performed. Suppose that SST = 94.8 and SSTR = 54.6. Find
the value of the third sum of squares, give its notation, state its name and the source of
variation it represents.

Question 40

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach.
At the 0.01 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the three different brands ? The sample
data are given below.

Question 41

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
At the 0.025 significance level, do the data provide sufficient evidence to conclude that a
difference exists between the population means of the three different brands? The sample
data are given below.

Question 42

Perform a Kruskal-Wallis test using the critical-value approach.
Four different types of fertilizers are used on raspberry plants. The number of raspberries
on each randomly selected plant is given below. Use the Kruskal-Wallis test to test the
claim that there is no difference in the distribution of the population

Question 43

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach.
The data below represent the weight losses for people on three different exercise programs. At the 1% significance level, does it appear that a difference exists in the true mean weight
loss produced by the three exercise programs?

Question 44

Find the required q-value.

Question 45

Provide an appropriate response.
Describe the null and alternate hypotheses for one-way ANOVA. Give an example.

Question 46

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach.
A consumer magazine wants to compare the lifetimes of ballpoint pens of three different
types. The magazine takes a random sample of pens of each type in the following table. Do the data indicate that there is a difference in mean lifetime for the three brands of
ballpoint pens? Us

Question 47

Provide an appropriate response.
A one-way ANOVA is to be performed. The following sample data are obtained. The common population standard deviation for the three populations is 2.5. Do you think
that the difference between the sample means could be due to variation within the
populations or does it seem clear that the difference between the sample means is due to a
difference between population means? Do you think that the null hypothesis would be
rejected? Explain your thinking.

Question 48

Determine the specified calculation.

Question 49

Conduct a Tukey multiple comparison. Display the confidence intervals in a table. State which population means can bedeclared different.
Perform a Tukey multiple comparison to compare the lifetimes of flashlight batteries of
three different brands. Use a family confidence level of 0.95. Independent random samples
of batteries of the three different brands yielded the following lifetimes in hours.

Question 50

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach.
Random samples of four different models of cars were selected and the gas mileage of each
car was measured. The results are shown below. Test the claim that the four different models have the same population mean. Use a
significance level of 0.05.

Question 51

Use Minitab to perform a Kruskal-Wallis test using the P-value approach.
A fire-science specialist tests three different brands of flares for their burning times (in
minutes)and the results are given below for the sample data. At the 0.05 significance level,
do the data provide sufficient evidence to conclude that a difference exists between the
mean burn times of the three different brands? Use the Kruskal-Wallis test.

Question 52

Compute the sum of squares.
A one-way ANOVA is to be performed. Independent random samples are selected from three different populations. The sample data are given in the table below. Compute the treatment sum of squares, SSTR.

A)246.0
B)66.0
C)100.2
D)21.0

Question 53

Provide an appropriate response.

Question 54

Find the required F-value.

Question 55

Provide an appropriate response.

Question 56

Provide an appropriate response.
List the basic properties of F-curves.

Question 57

Provide an appropriate response.
A one-way ANOVA is being performed. Suppose that SST = 120 and SSE = 70.3. Find the
value of the third sum of squares, give its notation, state its name and the source of
variation it represents.

Question 58

Determine the specified calculation.

Question 59

Provide an appropriate response.
A one-way ANOVA is performed to compare the means of four populations. If the null
hypothesis is not rejected, would it make sense to then perform a Tukey multiple
comparison? If the null hypothesis is rejected, would it make sense to then perform a
Tukey multiple comparison? Explain your reasoning. What can be determined from a
Tukey multiple comparison that cannot be determined from a one-way ANOVA?

Question 60

Perform a Kruskal-Wallis test using the critical-value approach.
A fire-science specialist tests three different brands of flares for their burning times (in
minutes)and the results are given below for the sample data. At the 0.05 significance level,
do the data provide sufficient evidence to conclude that a difference exists between the
mean burn times of the three different brands? Use the Kruskal-Wallis test.

Question 61

Provide an ap propriate response.
True or false: In a one-way ANOVA, if the null hypothesis is rejected, we conclude that the
population means are all different (i.e., no two of the population means are equal).

Question 62

Provide an ap propriate response.

Question 63

Compute the value of the H test statistic.
A Kruskall-Wallis test is to be performed to compare three population means. Independent random samples are selected from three different populations. The sample data are given in the
Table below.

Question 64

Compute the sum of squares.
A one-way ANOVA is to be performed. Independent random samples are selected from four different populations. The sample data are given in the table below. Compute the treatment sum of squares, SSTR.

A)116.6
B)1.7
C)351.7
D)74.0

Question 65

Determine the specified calculation.

Question 66

Compute the sum of squares.
A one-way ANOVA is to be performed. Independent random samples are selected from four different populations. The sample data are given in the table below. Compute the error sum of squares, SSE.

A)68.0
B)19.9
C)48.1
D)108.6

Question 67

Find the required q-value.

Question 68

Find the required F-value.

Question 69

Provide an appropriate response.
A one-way ANOVA is performed to compare the means of three populations. The sample sizes are 10, 11, and 13. Determine the degrees of freedom for the F-statistic.

A)(2, 31)
B)(3, 31)
C)(31, 33)
D)(2, 33)

Question 70

Find the required F-value.
An F-curve has df = (6, 20). Find the F-value having area 0.10 to its right.

A)2.84
B)3.87
C)2.09
D)7.40

Question 71

Find the required q-value.