Ch. 12 - Analysis of Variance

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 12 - Analysis of Variance

Problem 12.CQ.5

Chapter 12, Problem 12.CQ.5

Cola Weights The displayed results from Exercise 1 are from one-way analysis of variance. What is it about this test that characterizes it as one-way analysis of variance instead of two-way analysis of variance?

Verified step by step guidance

Understand the concept of one-way analysis of variance (ANOVA): One-way ANOVA is used to compare the means of three or more independent groups based on one independent variable (factor). It tests whether there is a statistically significant difference between the group means.

Contrast this with two-way ANOVA: Two-way ANOVA involves two independent variables (factors) and examines the interaction between them, as well as their individual effects on the dependent variable.

Identify the key characteristic of the test in the problem: The test described in the problem involves only one independent variable (factor), which is why it is classified as one-way ANOVA.

Recognize the absence of interaction effects: In one-way ANOVA, there is no consideration of interaction effects between multiple factors, which is a defining feature of two-way ANOVA.

Conclude why this test is one-way ANOVA: Since the analysis focuses on a single factor affecting the dependent variable (cola weights), it is characterized as one-way ANOVA rather than two-way ANOVA.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

One-Way Analysis of Variance (ANOVA)

One-way ANOVA is a statistical method used to compare the means of three or more independent groups based on one independent variable. It tests the null hypothesis that all group means are equal, allowing researchers to determine if at least one group mean significantly differs from the others. This method is particularly useful when assessing the impact of a single factor on a dependent variable.

Two-Way Analysis of Variance (ANOVA)

Two-way ANOVA extends the one-way ANOVA by examining the influence of two independent variables on a dependent variable. It not only assesses the main effects of each factor but also evaluates the interaction effect between them. This allows for a more comprehensive understanding of how multiple factors may simultaneously affect the outcome.

Independent Variables

Independent variables are the factors or conditions that are manipulated or categorized in an experiment to observe their effect on a dependent variable. In the context of ANOVA, the number of independent variables determines whether the analysis is one-way or two-way. For one-way ANOVA, there is only one independent variable, while two-way ANOVA involves two independent variables.

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Related Practice

Textbook Question

In Exercises 5–16, use analysis of variance for the indicated test.

Clancy, Rowling, and Tolstoy Ease of Reading Pages were randomly selected from three books: The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J.K. Rowling, and War and Peace by Leo Tolstoy. Listed below are Flesch Reading Ease Scores for those pages. Use a 0.05 significance level to test the claim that pages from books by those three authors have the same mean Flesch Reading Ease score. Given that higher scores correspond to text that is easier to read, which author appears to be different, and how is that author different?

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Textbook Question

Quarters Assume that weights of quarters minted after 1964 are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g (based on U.S. Mint specifications).

b. If 25 quarters are randomly selected, find the probability that their mean weight is greater than 5.675 g.

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Textbook Question

Normal Quantile Plot The accompanying normal quantile plot was obtained from the longevity times of presidents. What does this graph tell us?

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Textbook Question

Cola Weights For the four samples described in Exercise 1, the sample of regular Coke has a mean weight of 0.81682 lb, the sample of Diet Coke has a mean weight of 0.78479 lb, the sample of regular Pepsi has a mean weight of 0.82410 lb, and the sample of Diet Pepsi has a mean weight of 0.78386 lb. If we use analysis of variance and reach a conclusion to reject equality of the four sample means, can we then conclude that any of the specific samples have means that are significantly different from the others?

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Textbook Question

Cola Weights Data Set 37 “Cola Weights and Volumes” in Appendix B lists the weights (lb) of the contents of cans of cola from four different samples: (1) regular Coke, (2) Diet Coke, (3) regular Pepsi, and (4) Diet Pepsi. The results from analysis of variance are shown in the Minitab display below. What is the null hypothesis for this analysis of variance test? Based on the displayed results, what should you conclude about H_knot. What do you conclude about equality of the mean weights from the four samples?

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Textbook Question

Win 4 Lottery Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.

b. Does the display depict a normal distribution? Why or why not? What should be the shape of the histogram?

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