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Chapter 13: Q. 2 (page 547)
State the four assumptions for one-way ANOVA, and explain how those assumptions can be checked.
The factorial ANOVA requires the following assumptions: (1) interval data for the dependent variable, (2) normality, (3) homoscedasticity, and (4) no multicollinearity.
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Doing Time. The Federal Bureau of Prisons publishes data in Statistical Report on the times served by prisoners released from federal institutions for the first time. Independent simple random samples of released prisoners for five different offence categories yielded the data on time served, in months, shown on the WeissStats site.
a. Obtain individual normal probability plots and the standard deviation of the samples.
b. Perform a residual analysis.
c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so. also do parts (d) and (e).
d. Use a one-way ANOVA test to decide, at the significance level, Whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations fewer than the samples were taken.
e. Interpret your results from part (d).
Suppose that the variable under consideration is normally distributed in each of two populations and that the population standard deviations are equal. Further, suppose that you want to perform a hypothesis test to decide whether the populations have different means, that is, whether . If independent simple random samples are used, identify two hypothesis-testing procedures that you can use to carry out the hypothesis test.
Following are the notations for the three sums of squares. State the name of each sum of squares and the source of variation each sum of squares represents.
a. SSE
b. SSTR
c. SST
In this problem, consider an F-curve with .
Identify the degrees of freedom for the numerator.
Copepod Cuisine. Copepods are tiny crustaceans that are an essential link in the estuarine food web. Marine scientists G. Weiss et al. at the Chesapeake Biological Laboratory in Maryland designed an experiment to determine whether dietary lipid (fat) content is important in the population growth of a Chesapeake Bay copepod. Their findings were published in the paper "Development and Lipid Composition of the Harpacticoid Copepod Nitocra Spinipes Reared on Different Diets" (Marine Ecology Progress Series, Vol. , pp. ). Independent random samples of copepods were placed in containers containing lipid-rich diatoms, bacteria, or leafy macroalgae. There was containers total with four replicates per diet. Five gravid (egg-bearing) females were placed in each container. After days, the number of copepods in each container was as follows.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean number of copepods among the three different diets? (Note:
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