Statistics Question 22.16

Describe the following situation in which we want to compare the mean responses in several populations.

• Identify the populations and the response variable

• Then give I , the n _i , and N .

• Give the degrees of freedom of the ANOVA F test.

A maker of detergents wants to compare the attractiveness to consumers of six package designs. Each package is shown to 120 different consumers who rate the attractiveness of the design on a 1 to 10 scale.

Statistics Question 22.22

How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, the dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay; lower strength means the fabric has decayed.

Part of the study buried 20 polyester strips in well-drained soil in the summer. Five of the strips, chosen at random, were dug up after 2 weeks; another 5 were dug up after 4 weeks, 8 weeks, and 16 weeks. Here are the breaking strengths in pounds.

1. Find the mean strength for each group and plot the means against time. Does it appear that polyester loses strength consistently over time after it is buried?
2. Find the standard deviations for each group. Do they meet our criterion for applying ANOVA?
3. The ANOVA F test extends the two-sample t test to more than two groups. Explain carefully why use of the two-sample t test for two of the groups is acceptable but using the t test on all four groups is not acceptable.
4. Do the ANOVA for the data anyway and state your conclusion based on the ANOVA p-value.

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