Deck 8: Anova to Compare Means

Question 1

Use the following
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the population means. Give a brief reason, comparing means and variability, for your answer.
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Answer 1

Dataset A is likely to provide stronger evidence of differences among the population means because the sample means are further apart than those in Dataset B. The variability within each sample for the two datasets is similar.

Question 2

Use the following
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the population means. Give a brief reason, comparing means and variability, for your answer.
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Answer 2

Dataset B is likely to provide stronger evidence of differences among the population means because, while the sample means within each group are the same for both datasets, there is much less variability within each group in Dataset B than there is in Dataset A.

Question 3

Use the following
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the population means. Give a brief reason, comparing means and variability, for your answer.
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Answer 3

Dataset A is likely to provide stronger evidence of differences among the population means because, while the sample means within each group look to be about the same for both datasets, there is much less variability within each group in Dataset A than there is in Dataset B.

Question 4

Use the following
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the population means. Give a brief reason, comparing means and variability, for your answer.
-

Question 5

Use the following
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the population means. Give a brief reason, comparing means and variability, for your answer.

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Question 6

Use the following
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the population means. Give a brief reason, comparing means and variability, for your answer.
-

Question 7

Use the following
A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours.

-Are the conditions for using ANOVA reasonably satisfied? Explain briefly.

Question 8

Use the following
A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours.

-Complete the ANOVA table below for doing this test using the template started below. Use two decimal places in the F statistic.

Question 9

Use the following
A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours.

-Use the F-distribution to find the p-value for the test. Using = 0.05, does the mean electricity usage differ significantly by day of the week? Make a conclusion in context.

Question 10

Use the following
A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours.

-Computer output from the analysis is provided:
One-way ANOVA: Electricity versus Day of Week

What is the F-statistic? What is the p-value? Using = 0.05, what is the conclusion of the text, in context?

Question 11

Use the following
A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours.

-Use the data and ANOVA results to construct a 95% confidence interval for the difference in mean electricity use between Saturdays and Sundays. Round the margin of error to two decimal places. Does your interval suggest that a significant difference in mean electricity use for these two days? Briefly explain.

Question 12

Use the following
A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours.

-Based on the ANOVA results, test at the 5% level whether the data provide evidence of a difference in mean electricity use on Sundays and Mondays. Use three decimal places in the test statistic.

Question 13

Use the following
A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours.

-Computer output provides the following grouping information:

Means that do not share a letter are significantly different.
Use the output to make a statement about how electricity usage differs significantly by day of the week.

Question 14

Use the following
Penalties in ice hockey occur when a player breaks one of the rules of the game. In most cases, when a penalty occurs, the offending player is placed in the penalty box (the length of time spent in the penalty box depends on the severity of the penalty), and the team has to play with fewer people on the ice, which can result in an advantage for the opposing team. The number of penalties per game for several randomly selected games are displayed for three college men's ice hockey teams.

-Use the summary information to compute the three sums of squares needed for using ANOVA to test for a difference in mean number of penalties among these three teams. Round each to two decimal places.

Question 15

Use the following
Penalties in ice hockey occur when a player breaks one of the rules of the game. In most cases, when a penalty occurs, the offending player is placed in the penalty box (the length of time spent in the penalty box depends on the severity of the penalty), and the team has to play with fewer people on the ice, which can result in an advantage for the opposing team. The number of penalties per game for several randomly selected games are displayed for three college men's ice hockey teams.

-Construct the ANOVA table and test, at the 5% significance level, for a difference in mean number of penalties among these three hockey teams. Use two decimal places when rounding decimal values. Include the details of your test.

Question 16

Use the following
Penalties in ice hockey occur when a player breaks one of the rules of the game. In most cases, when a penalty occurs, the offending player is placed in the penalty box (the length of time spent in the penalty box depends on the severity of the penalty), and the team has to play with fewer people on the ice, which can result in an advantage for the opposing team. The number of penalties per game for several randomly selected games are displayed for three college men's ice hockey teams.

-Computer output from the analysis is provided:
One-way ANOVA: Penalties versus Team

What is the F-statistic? What is the p-value? Using, = 0.05, what is the conclusion of the test, in context?

Question 17

Use the following
Penalties in ice hockey occur when a player breaks one of the rules of the game. In most cases, when a penalty occurs, the offending player is placed in the penalty box (the length of time spent in the penalty box depends on the severity of the penalty), and the team has to play with fewer people on the ice, which can result in an advantage for the opposing team. The number of penalties per game for several randomly selected games are displayed for three college men's ice hockey teams.

-Use the summary information and results from the ANOVA to construct 95% confidence intervals for the differences in each pair of means:
(a) Team A and Team B
(b) Team A and Team C
(c) Team B and Team C
In each case, round the margin of error to two decimal places. Based on your work, which teams have significantly different means? Briefly justify your answer.

Question 18

Use the following
Penalties in ice hockey occur when a player breaks one of the rules of the game. In most cases, when a penalty occurs, the offending player is placed in the penalty box (the length of time spent in the penalty box depends on the severity of the penalty), and the team has to play with fewer people on the ice, which can result in an advantage for the opposing team. The number of penalties per game for several randomly selected games are displayed for three college men's ice hockey teams.

-Computer output provides the following information about the pairwise differences:

Based on this output, which teams have significantly different means? Briefly justify your answer.

Question 19

Use the following
Penalties in ice hockey occur when a player breaks one of the rules of the game. In most cases, when a penalty occurs, the offending player is placed in the penalty box (the length of time spent in the penalty box depends on the severity of the penalty), and the team has to play with fewer people on the ice, which can result in an advantage for the opposing team. The number of penalties per game for several randomly selected games are displayed for three college men's ice hockey teams.

-Computer output provides the following grouping information:

Means that do not share a letter are significantly different.
Based on this output, which teams have significantly different means? Briefly justify your answer.

Question 20

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-State the appropriate null and alternative hypotheses for testing if the mean calories per serving differs among the three brands.

Question 21

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Are the conditions for using ANOVA reasonably satisfied? Explain briefly.

Question 22

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Computer output from the analysis is provided:
One-way ANOVA: Calories versus Brand

What is the F-statistic? What is the p-value? Using = 0.05, what is the conclusion of the test, in context?

Question 23

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Use the summary information and the fact that the sums of squares for groups is SSG = 27,476 and for error is SSTotal = 152,379 to complete an ANOVA table and find the F-statistic. Round decimal answers to two decimal places.

Question 24

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Use the F-distribution to find the p-value and state the conclusion of the test in context (using = 0.05).

Question 25

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Computer output from Minitab is provides the following information about the pairwise differences:
Brand = General Mills subtracted from:

Brand = Kashi subtracted from:

Based on this output, which brands have significantly different means? Briefly justify your answer.

Question 26

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Computer output provides the following grouping information:

Means that do not share a letter are significantly different.
Based on this output, which brands have significantly different means? Briefly justify your answer.

Question 27

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the number of calories per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Use the summary information and results from the ANOVA to test for significant differences (using = 0.05) in each pair of means:
(a) General Mills and Kashi
(b) General Mills and Kellogg's
(c) Kashi and Kellogg's
In each case, round the test statistic to three decimal places. Based on your work, which brands have significantly different means? Briefly justify your answer.

Question 28

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the amount of sugar (g) per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Are the conditions for using ANOVA reasonably satisfied? Explain briefly.

Question 29

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the amount of sugar (g) per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Computer output from the analysis is provided:
One-way ANOVA: Sugar (g) versus Brand

Test, at the 5% level, if there is evidence that the average amount of sugar per serving differs significantly among the three brands. Include all details of the test.

Question 30

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the amount of sugar (g) per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Use the summary information to compute the three sums of squares needed for using ANOVA to test for a difference in the mean amount of calories per serving among the three brands. Round each to two decimal places.

Question 31

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the amount of sugar (g) per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Construct the ANOVA table and test, at the 5% significance level, for a difference in mean amount of sugar among the three brands. Use two decimal places in all decimal values. Include all details of the test.

Question 32

Use the following
Breakfast is often considered to be the most important meal of the day. Data on the amount of sugar (g) per serving for randomly selected cereals from three different brands (General Mills, Kellogg's, and Kashi) are summarized in the provided plot and table.


-Should you conduct inference after the ANOVA to investigate differences among the pairs of means in this situation? Briefly explain why or why not.

Question 33

Use the following
An environmental studies student working on an independent research project was investigating metal contamination in the St. Lawrence River. The metals can accumulate in organisms that live in the river (known as bioaccumulation). He collected samples of Quagga mussels at three sites in the St. Lawrence River and measured the concentration of copper (in micrograms per gram, or mcg/g) in the mussels. His data are summarized in the provided table and plot. He wants to know if there are any significant differences in mean copper concentration among the three sites


-Are the conditions for using ANOVA reasonably satisfied? Explain briefly.

Question 34

Use the following
An environmental studies student working on an independent research project was investigating metal contamination in the St. Lawrence River. The metals can accumulate in organisms that live in the river (known as bioaccumulation). He collected samples of Quagga mussels at three sites in the St. Lawrence River and measured the concentration of copper (in micrograms per gram, or mcg/g) in the mussels. His data are summarized in the provided table and plot. He wants to know if there are any significant differences in mean copper concentration among the three sites


-Use the summary information to compute the three sums of squares needed for using ANOVA to test for a difference in mean copper concentration among the three sites. Round each to two decimal places.

Question 35

Use the following
An environmental studies student working on an independent research project was investigating metal contamination in the St. Lawrence River. The metals can accumulate in organisms that live in the river (known as bioaccumulation). He collected samples of Quagga mussels at three sites in the St. Lawrence River and measured the concentration of copper (in micrograms per gram, or mcg/g) in the mussels. His data are summarized in the provided table and plot. He wants to know if there are any significant differences in mean copper concentration among the three sites


-Construct the ANOVA table and test, using = 0.05, for a difference in mean copper concentration among the three sites. Round decimal values to two decimal places. Include all details of the test

Question 36

Use the following
An environmental studies student working on an independent research project was investigating metal contamination in the St. Lawrence River. The metals can accumulate in organisms that live in the river (known as bioaccumulation). He collected samples of Quagga mussels at three sites in the St. Lawrence River and measured the concentration of copper (in micrograms per gram, or mcg/g) in the mussels. His data are summarized in the provided table and plot. He wants to know if there are any significant differences in mean copper concentration among the three sites


-Computer output from the analysis is provided:
One-way ANOVA: Copper Concentration (mcg/g) versus Sit

Test, using = 0.05, for a difference in mean copper concentration among the three sites. Include all details of the test

Question 37

Use the following
An environmental studies student working on an independent research project was investigating metal contamination in the St. Lawrence River. The metals can accumulate in organisms that live in the river (known as bioaccumulation). He collected samples of Quagga mussels at three sites in the St. Lawrence River and measured the concentration of copper (in micrograms per gram, or mcg/g) in the mussels. His data are summarized in the provided table and plot. He wants to know if there are any significant differences in mean copper concentration among the three sites


-Use the summary information and results from the ANOVA to construct 95% confidence intervals for the differences in each pair of means:
(a) Site 1 and Site 2
(b) Site 1 and Site 3
(c) Site 2 and Site 3
In each case, round the margin of error to two decimal places. Based on your work, which sites have significantly different means? Briefly justify your answer.
Because this confidence interval contains 0, there is no evidence that Sites 2 and 3 have significantly different mean concentrations of copper.

Question 38

Use the following
An environmental studies student working on an independent research project was investigating metal contamination in the St. Lawrence River. The metals can accumulate in organisms that live in the river (known as bioaccumulation). He collected samples of Quagga mussels at three sites in the St. Lawrence River and measured the concentration of copper (in micrograms per gram, or mcg/g) in the mussels. His data are summarized in the provided table and plot. He wants to know if there are any significant differences in mean copper concentration among the three sites


-Computer output from the analysis provides the following information about the pairwise differences:
Site = 1 subtracted from
I
Site = 2 subtracted from

Based on this output, which sites have significantly different means? Briefly justify your answer.

Question 39

Use the following
An environmental studies student working on an independent research project was investigating metal contamination in the St. Lawrence River. The metals can accumulate in organisms that live in the river (known as bioaccumulation). He collected samples of Quagga mussels at three sites in the St. Lawrence River and measured the concentration of copper (in micrograms per gram, or mcg/g) in the mussels. His data are summarized in the provided table and plot. He wants to know if there are any significant differences in mean copper concentration among the three sites


-Computer output from the analysis provides the following grouping information

Means that do not share a letter are significantly different.
Based on this output, which sites have significantly different means? Briefly justify your answer.

Question 40

Analysis of variance is used to test for significant differences among

A) means.
B) variances.
C) standard deviations.
D) proportions.

Question 41

Some computer output from an analysis of variance is provided.

How many groups are there?

A) 3
B) 4
C) 5
D) 6

Question 42

Some computer output from an analysis of variance is provided.

What is the overall sample size?

A) 125
B) 124
C) 123
D) 121

Question 43

A scientist performing analysis of variance has the following null hypothesis:

What is the appropriate alternative hypothesis for his analysis?

A)
B)
C)
D) H_a: At least one

Question 44

SSE = SSTotal + SSG

Question 45

Use the following
The sample sizes for the groups in a dataset and an outline of an analysis of variance table with partial information are provided. Fill in the missing parts of the table. Round decimal answers to two decimal places.
-Three groups with n₁ = 10, n₂ = 10, and n₃ = 10.

Question 46

Use the following
The sample sizes for the groups in a dataset and an outline of an analysis of variance table with partial information are provided. Fill in the missing parts of the table. Round decimal answers to two decimal places.
-Four groups with n₁ = 6, n₂ = 5, n₃ = 5, and n₄ = 4.

Question 47

Use the following
The sample sizes for the groups in a dataset and an outline of an analysis of variance table with partial information are provided. Fill in the missing parts of the table. Round decimal answers to two decimal places.
-Three groups with n₁ = 8, n₂ = 7, and n₃ = 5.

Question 48

Use the following
Summary statistics from a dataset and the corresponding computer analysis of variance output are provided.



-What is the pooled standard deviation?

A) 24.9
B) 4.99
C) 16.90
D) 42.34

Question 49

Use the following
Summary statistics from a dataset and the corresponding computer analysis of variance output are provided.



-What degrees of freedom are used in doing inferences for these means and differences in means after ANOVA?

A) 2
B) 3
C) 72
D) 74

Question 50

Use the following
Summary statistics from a dataset and the corresponding computer analysis of variance output are provided.


-Find a 90% confidence interval for the mean of population A. Round the margin of error to three decimal places.

Question 51

Use the following
Summary statistics from a dataset and the corresponding computer analysis of variance output are provided.


-Find a 95% confidence interval for the difference in the means of Populations A and B. Round the margin of error to three decimal places.

Question 52

Use the following
Summary statistics from a dataset and the corresponding computer analysis of variance output are provided.


-Test for a difference in population means between groups A and C. Use = 0.05 and show all details of the test. Round the test statistic to two decimal places.