Exam 8: Anova to Compare Means

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.

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.

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.

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. -

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?

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.

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.

A scientist performing analysis of variance has the following null hypothesis: What is the appropriate alternative hypothesis for his analysis?

Some computer output from an analysis of variance is provided. How many groups are there?

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.

SSE = SSTotal + SSG

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.

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?

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.

Some computer output from an analysis of variance is provided. What is the overall sample size?

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.

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.

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.

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.

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.