Data set: PaperTowel
As a final project in an introductory statistics class, several students decided to conduct a study to test the strength of paper towels. Television advertisements had claimed that a certain brand of paper towel was the strongest, and these students wanted to determine if there really was a difference. The students purchased rolls of towels at a local store and sampled 26 towels from 3 brands of paper towels: Bounty, Comfort, and Decorator. Before any data were collected, these students determined that the following should be held as constant as possible throughout the study: • 15 drops of water were applied to the center of each towel.
• Paper towels were selected that had the same size.
• The towels were held at all four corners by two people.
• Weights (10, 25, 50, or 100 grams) were slowly added to the center of each towel by a third person until it broke.
• The order in which the 26 paper towels were tested was randomized.
The file PaperTowel shows the breaking Strength of each towel. Breaking Strength is defined as the total weight that each towel successfully held. The next additional weight caused the towel to break. a. For this paper towel study, identify the explanatory variable, the observational units (experimental units or subjects), and the response variable. Write out (in words and symbols) appropriate null and alternative hypotheses.
b. Graph the data and compare the center and spread of the breaking strength of each of the three brands. Does any group have outliers or skewed data?
c. Conduct an ANOVA. The null hypothesis is H0: µ1 = µ2 = µ3 versus the alternative Ha: at least one mean is different from another. Does the ANOVA show that a significant difference exists between brands?
d. Show that the equal variance assumption is violated in this study. Instead of using Strength as the response variable, use the natural log of Strength to conduct an ANOVA. The null hypothesis is still stated as H0: µ1 = µ2 = µ3 versus the alternative Ha: at least one mean is different from another. Does the ANOVA show that a significant difference exists between brands?
e. Compare residual plots and the group standard deviations from the Strength and ln( Strength) F- tests. Which test should be used to state your conclusions? Explain.
f. Assume the students purchased one roll of Bounty paper towels and randomly selected 26 sheets from that one roll. The same holds true for other brands. What is the population for which the results of this study can hold?
g. Assume the students randomly purchased 26 rolls of Bounty paper towels from various stores and randomly selected one sheet from each roll. The same holds true for other brands. What is the population for which the results of this study can hold?