Deck 11: Analysis of Variance

Question 1

Use the following sample data to answer the next questions. For a study on
Type 1 diabetes, medical graduate students subdivided the United States into four
study regions (Northeast, Southeast, Southwest, and Northwest). The students
randomly selected seven patients per region and recorded the number of times
during a randomly selected month that each patient used insulin shots to regulate
blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the
claim that the means from the different regions are not the same.
Mean number of times patients used insulin shots to regulate blood sugar levels

Determine the value of the F test statistic.

Answer 1

test statistic F = 9.94

Question 2

Determine whether the following statement is true or false.
Assuming calculations for a One-Way ANOVA with equal sample sizes, if each data value in one of the samples is increased by a fixed amount, then any change in the F test statistic and the P-value is attributable only to the change in the sample mean.

Answer 2

True

Question 3

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Wildlife biologists studying beaver habitats measured the number
of beaver colonies per square mile identified at two randomly selected wetland
habitats, under three densities of tree growth (sparse, average, or dense growth).
Use a .05 significance level.
For the density effect, state a conclusion about the null hypothesis.

Answer 3

Reject .

Question 4

Use the following sample data to answer the next questions. For a study on
Type 1 diabetes, medical graduate students subdivided the United States into four
study regions (Northeast, Southeast, Southwest, and Northwest). The students
randomly selected seven patients per region and recorded the number of times
during a randomly selected month that each patient used insulin shots to regulate
blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the
claim that the means from the different regions are not the same.
Mean number of times patients used insulin shots to regulate blood sugar levels

State a final conclusion that addresses the original claim.

Question 5

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Wildlife biologists studying beaver habitats measured the number
of beaver colonies per square mile identified at two randomly selected wetland
habitats, under three densities of tree growth (sparse, average, or dense growth).
Use a .05 significance level.
For the interaction effect, state a conclusion about the null hypothesis.

Question 6

Determine whether the following statement is true or false.
Assuming that differences exist among the population means, the One-Way ANOVA can determine which population mean(s) differ from the others.

Question 7

Determine whether the following statement is true or false.
One method to reduce the effect of extraneous factors is to design the experiment so that it has a completely randomized design.

Question 8

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Wildlife biologists studying beaver habitats measured the number
of beaver colonies per square mile identified at two randomly selected wetland
habitats, under three densities of tree growth (sparse, average, or dense growth).
Use a .05 significance level.
State a final conclusion about the overall study.

Question 9

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Wildlife biologists studying beaver habitats measured the number
of beaver colonies per square mile identified at two randomly selected wetland
habitats, under three densities of tree growth (sparse, average, or dense growth).
Use a .05 significance level.
For the site effect, state a conclusion about the null hypothesis.

Question 10

Determine whether the following statement is true or false.
If there is only one observation per cell in a Two-Way ANOVA, and it can be assumed there is an interaction between factors, then we can proceed to interpret the results of the row and column effects.

Question 11

Use the following sample data to answer the next questions. For a study on
Type 1 diabetes, medical graduate students subdivided the United States into four
study regions (Northeast, Southeast, Southwest, and Northwest). The students
randomly selected seven patients per region and recorded the number of times
during a randomly selected month that each patient used insulin shots to regulate
blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the
claim that the means from the different regions are not the same.
Mean number of times patients used insulin shots to regulate blood sugar levels

Identify the

Question 12

Use the following sample data to answer the next questions. For a study on
Type 1 diabetes, medical graduate students subdivided the United States into four
study regions (Northeast, Southeast, Southwest, and Northwest). The students
randomly selected seven patients per region and recorded the number of times
during a randomly selected month that each patient used insulin shots to regulate
blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the
claim that the means from the different regions are not the same.
Mean number of times patients used insulin shots to regulate blood sugar levels

Identify the alternative hypothesis.

Question 13

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Wildlife biologists studying beaver habitats measured the number
of beaver colonies per square mile identified at two randomly selected wetland
habitats, under three densities of tree growth (sparse, average, or dense growth).
Use a .05 significance level.
For the interaction effect, identify the null hypothesis, the value of the F test statistic, and the .

Question 14

Use the following sample data to answer the next questions. For a study on
Type 1 diabetes, medical graduate students subdivided the United States into four
study regions (Northeast, Southeast, Southwest, and Northwest). The students
randomly selected seven patients per region and recorded the number of times
during a randomly selected month that each patient used insulin shots to regulate
blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the
claim that the means from the different regions are not the same.
Mean number of times patients used insulin shots to regulate blood sugar levels

Identify the null hypothesis.

Question 15

Use the following sample data to answer the next questions. For a study on
Type 1 diabetes, medical graduate students subdivided the United States into four
study regions (Northeast, Southeast, Southwest, and Northwest). The students
randomly selected seven patients per region and recorded the number of times
during a randomly selected month that each patient used insulin shots to regulate
blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the
claim that the means from the different regions are not the same.
Mean number of times patients used insulin shots to regulate blood sugar levels

State a conclusion about the null hypothesis.

Question 16

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Wildlife biologists studying beaver habitats measured the number
of beaver colonies per square mile identified at two randomly selected wetland
habitats, under three densities of tree growth (sparse, average, or dense growth).
Use a .05 significance level.
For the density effect, identify the null hypothesis, the value of the F test statistic, and the .

Question 17

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Wildlife biologists studying beaver habitats measured the number
of beaver colonies per square mile identified at two randomly selected wetland
habitats, under three densities of tree growth (sparse, average, or dense growth).
Use a .05 significance level.
For the site effect, identify the null hypothesis, the value of the F test statistic, and the

Question 18

Determine whether the following statement is true or false.
The reason we cannot use two One-Way ANOVAs instead of using a Two-Way ANOVA is that this would ignore the effect of interaction between the two factors.

Question 19

Determine whether the following statement is true or false.
For a Two-Way ANOVA, assuming there is an interaction, we can continue to interpret the results of the row and column effects.

Question 20

Determine whether the following statement is true or false.
The reason we cannot use multiple t-tests to claim that four populations have the same mean is that we increase the likelihood of a type II error.

Question 21

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Biologists studying habitat use in Lepidopteran moths measured
the number of savannah moths found at three randomly selected prairie sites with
two potential habitat interferences (expansion of row crops and grazing). Use a .05
significance level.
For the habitat effect, state a conclusion about the null hypothesis.

Question 22

Use the following sample data to answer the next questions. Geneticists
studying carriers of genetic diseases followed subjects subdivided by race.
Researchers randomly selected seven patients per race who had been identified as
carrying a certain gene for a genetic disease; these patients were followed to
determine the number of their siblings who also carried the gene for the genetic
disease. Use a One-Way ANOVA at a .05 significance level to test the claim that
the means from the different races are not all the same.
Identify the alternative hypothesis.

Question 23

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Biologists studying habitat use in Lepidopteran moths measured
the number of savannah moths found at three randomly selected prairie sites with
two potential habitat interferences (expansion of row crops and grazing). Use a .05
significance level.
State a final conclusion about the overall study.

Question 24

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Biologists studying habitat use in Lepidopteran moths measured
the number of savannah moths found at three randomly selected prairie sites with
two potential habitat interferences (expansion of row crops and grazing). Use a .05
significance level.
For the site effect, state a conclusion about the null hypothesis.

Question 25

Determine whether the following statement is true or false.
Assuming calculations for a One-Way ANOVA with equal sample sizes, if each data value in one of the samples is increased by a fixed amount, then any change in the F test statistic and the P-value is attributable only to the change in the sample variances.

Question 26

Use the following sample data to answer the next questions. Geneticists
studying carriers of genetic diseases followed subjects subdivided by race.
Researchers randomly selected seven patients per race who had been identified as
carrying a certain gene for a genetic disease; these patients were followed to
determine the number of their siblings who also carried the gene for the genetic
disease. Use a One-Way ANOVA at a .05 significance level to test the claim that
the means from the different races are not all the same.
State a final conclusion that addresses the original claim.

Question 27

Determine whether the following statement is true or false.
Assuming differences exist among the population means, the Bonferroni test can determine which population means differ from the others.

Question 28

Determine whether the following statement is true or false.
If there is only one observation per cell in a Two-Way ANOVA, and it can be assumed there is not an interaction between factors, then we can proceed to interpret the results of the row and column effects.

Question 29

Determine whether the following statement is true or false.
The reason we cannot use multiple t-tests to claim that four populations have the same mean is that we increase the likelihood of a type I error.

Question 30

Determine whether the following statement is true or false.
Another way to conduct a Two-Way ANOVA is to conduct two separate One-Way ANOVAs.

Question 31

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Biologists studying habitat use in Lepidopteran moths measured
the number of savannah moths found at three randomly selected prairie sites with
two potential habitat interferences (expansion of row crops and grazing). Use a .05
significance level.
For the interaction effect, state a conclusion about the null hypothesis.

Question 32

Determine whether the following statement is true or false.
For a Two-Way ANOVA, assuming there is not an interaction, we can continue to interpret the results of the row and column effects.

Question 33

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Biologists studying habitat use in Lepidopteran moths measured
the number of savannah moths found at three randomly selected prairie sites with
two potential habitat interferences (expansion of row crops and grazing). Use a .05
significance level.
For the interaction effect, identify the null hypothesis, the value of the F test statistic, and the

Question 34

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Biologists studying habitat use in Lepidopteran moths measured
the number of savannah moths found at three randomly selected prairie sites with
two potential habitat interferences (expansion of row crops and grazing). Use a .05
significance level.
For the site effect, identify the null hypothesis, the value of the F test statistic, and the

Question 35

Use the following sample data to answer the next questions. Geneticists
studying carriers of genetic diseases followed subjects subdivided by race.
Researchers randomly selected seven patients per race who had been identified as
carrying a certain gene for a genetic disease; these patients were followed to
determine the number of their siblings who also carried the gene for the genetic
disease. Use a One-Way ANOVA at a .05 significance level to test the claim that
the means from the different races are not all the same.
State a conclusion about the null hypothesis.

Question 36

Determine whether the following statement is true or false.
One method to reduce the effect of extraneous factors is to design the experiment so that it has a convenience sampling design.

Question 37

Use the following sample data to answer the next questions. Geneticists
studying carriers of genetic diseases followed subjects subdivided by race.
Researchers randomly selected seven patients per race who had been identified as
carrying a certain gene for a genetic disease; these patients were followed to
determine the number of their siblings who also carried the gene for the genetic
disease. Use a One-Way ANOVA at a .05 significance level to test the claim that
the means from the different races are not all the same.
Identify the .

Question 38

Use the following technology display from a Two-Way ANOVA to answer the next
questions. Biologists studying habitat use in Lepidopteran moths measured
the number of savannah moths found at three randomly selected prairie sites with
two potential habitat interferences (expansion of row crops and grazing). Use a .05
significance level.
For the habitat effect, identify the null hypothesis, the value of the F test statistic, and the

Question 39

Use the following sample data to answer the next questions. Geneticists
studying carriers of genetic diseases followed subjects subdivided by race.
Researchers randomly selected seven patients per race who had been identified as
carrying a certain gene for a genetic disease; these patients were followed to
determine the number of their siblings who also carried the gene for the genetic
disease. Use a One-Way ANOVA at a .05 significance level to test the claim that
the means from the different races are not all the same.
Identify the null hypothesis.

Question 40

Use the following sample data to answer the next questions. Geneticists
studying carriers of genetic diseases followed subjects subdivided by race.
Researchers randomly selected seven patients per race who had been identified as
carrying a certain gene for a genetic disease; these patients were followed to
determine the number of their siblings who also carried the gene for the genetic
disease. Use a One-Way ANOVA at a .05 significance level to test the claim that
the means from the different races are not all the same.
Determine the value of the F test statistic.