Week 10 Assignment:

  1. Under Section 10-2, page 584, do problem 1.

Readability of Authors

The Chapter Problem uses the Flesch Reading Ease score for randomly selected pages from books by Tom Clancy, J.K. Rowling, and Leo Tolstoy. If the Flesch-Kincaid Grade Level scores are used instead (see Data Set 14 in Appendix C), the analysis of variance results from Minitab are as shown in the accompanying table. Assume that we want to use a 0.05 significance level in testing the null hypothesis that the three authors have Flesch-Kincaid Grade Level scores with the same mean.

Minitab
Analysis of Variance
Source / DF / SS / MS / F / P
Factor / 2 / 68.19 / 34.09 / 8.98 / 0.001
Error / 33 / 125.31 / 3.80
Total / 35 / 193.50
  1. What is the null hypothesis?
  1. What is the alternative hypothesis?
  1. Identify the value of the test statistic.

F = 8.98

2. Under Section 10-2, page 584, do problem 2.

Fabric Flammability Tests in Different Laboratories

Flammability tests were conducted on children’s sleepwear. The Vertical Semirestrained Test was used, in which pieces of fabric were burned under controlled conditions. After the burning stopped, the length of the charred portion was measured and recorded. The same fabric samples were tested at five different laboratories. The analysis of variance results from Excel are shown below

Excel
Source of Variation / SS / df / MS / F / P-value / F crit
Between Groups / 2.087194264 / 4 / 0.521798566 / 2.949333035 / 0.030665893 / 2.588834036
Within Groups / 7.607597403 / 43 / 0.17692087
Total / 9.694791667 / 47
  1. What is the null hypothesis?
  1. What is the alternative hypothesis?
  1. Identify the value of the test statistic.

F = 2.949333035

  1. Find the critical value for a 0.05 significance level.

F = 2.588834036

  1. Identify the P-value

P-value = 0.030665893

  1. Is there sufficient evidence to support the claim that the means for the different laboratories are not all the same?

Yes, since the P-value < 0.05.

  1. Under Section 10-3, page 594, do problem 1.

Meaning of Two-Way ANOVA

The method of this section is referred to as a two-way analysis of variance, or two-way ANOVA. Why is the term two-way used? Why is the term analysis of variance used?

Answer: There are two factors.

Answer: The test statistic (F) is the ratio of two different variances.

4. Under Section 10-3, page 594, do problem 2.

Why Not One-Way ANOVA?

The given Minitab display results from measured amounts of DDT in falcons partitioned into nine cells according to one factor of location and another factor of age of the falcon. Each cell includes three DDT measurements. Why can’t we conduct a thorough analysis of the data by simply executing two separate tests using one-way ANOVA (described in Section 10-2), where one test addresses the differences in sites and the other test addresses the differences in age? That is, why is a two-way ANOVA required instead of two separate applications of one-way ANOVA?

Answer: A two-way ANOVA tests for interaction among the two factors. Plus the alpha level is affected when doing multiple tests.