Question 1

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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.

Accepted Answer

The answer of Use the following to answer the questions...

Question 2

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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, μg/g 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?

Accepted Answer

Yes. The boxplots indicate that the data for all groups is reasonably symmetric and without outliers. The standard deviation for each group is not more than twice the standard deviation for another group.

Question 3

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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, μg/g 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.

Accepted Answer

The answer of Use the following to answer the questions...

Question 4

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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, μg/g 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 α = 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.

Accepted Answer

The answer of Use the following to answer the questions...

Question 5

Use the following to answer the questions below:
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, μg/g 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 gives a p-value of 0.011. Test, using α = 0.05, for a difference in mean copper concentration among the three sites. Include all details of the test.

Accepted Answer

The answer of Use the following to answer the questions...

Question 6

Use the following to answer the questions below:
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, μg/g 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.

Accepted Answer

The answer of Use the following to answer the questions...

Question 7

Use the following to answer the questions below:
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, μg/g 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:

Site = 2 subtracted from:

Based on this output, which sites have significantly different means?
A) Only Sites 1 and 3 have significantly different means.
B) Only Sites 1 and 2 have significantly different means.
C) Only Sites 2 and 3 have significantly different means.
D) None of the sites have significantly different means.

Accepted Answer

Only Sites 1 and 3 have significantly different means because that is the only confidence interval that does not contain 0. Because the interval contains entirely negative values, there is evidence that Site 1 has a significantly larger mean concentration of copper than Site 3.

Question 8

Use the following to answer the questions below:
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, μg/g 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.
A) Only Sites 1 and 3 have significantly different means.
B) Only Sites 1 and 2 have significantly different means.
C) Only Sites 2 and 3 have significantly different means.
D) None of the sites have significantly different means.

Accepted Answer

Only Sites 1 and 3 have significantly different means because that is the only pair that do not share a letter. Because Site 1 has the larger sample mean in the pair, there is evidence that Site 1 has a significantly larger mean concentration of copper than Site 3.

Question 9

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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

Accepted Answer

The pooled standard deviation is a weighted average of standard deviations from two or more groups, often used in t-tests. The value 4.99 is a typical result for such calculations.

Question 10

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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

Accepted Answer

The degrees of freedom for error in ANOVA is typically the total number of observations minus the number of groups, which is often the largest value in the context of ANOVA tables.

Question 11

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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.
A) 35.040 to 38.366
B) 35.061 to 38.345
C) 34.747 to 38.660
D) 34.937 to 38.470

Accepted Answer

The correct answer is A because the confidence interval is 35.040 to 38.366, and the margin of error is (38.366 - 35.040) / 2 = 1.663, which rounds to 1.663.

Question 12

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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.
A) 4.333 to 9.035
B) 4.362 to 9.006
C) 3.918 to 9.405
D) 4.191 to 9.177

Accepted Answer

(36.703 - 30.019) ± 1.666 11eeb2d3_8e07_bf66_b9aa_831f5a174a60_TBW1049_00 
6.684 ± 1.666(1.411382)
6.684 ± 2.351
4.333 to 9.035

Question 13

Use the following to answer the questions below:
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 α = 0.05 and show all details of the test. Round the test statistic to two decimal places.

Accepted Answer

The answer of Use the following to answer the questions...

Quiz 8: Anova to Compare Means

Use the following to answer the questions below: Summary statistics from a dataset and the corresponding computer analysis of variance output are provided. -What is the pooled standard deviation?

Use the following to answer the questions below: 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?

Use the following to answer the questions below: 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.

Use the following to answer the questions below: 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.