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Chapter 13: Q. 13.32 (page 542)
Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are and Determine the degrees of freedom for the statistic.
The degrees of freedom for suchstatistics are
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Staph Infections. In the article "Using EDE, ANOVA and Regression to Optimize Some Microbiology Data" (Journal of Statistics Education, Vol. , No. 2, online), N. Binnie analyzed bacteria culture data collected by G. Cooper at the Auckland University of Technology. Five strains of cultured Staphylococcus aureus bacteria that cause staph infections were observed for hours at . The following table reports bacteria counts, in millions, for different cases from each of the five strains.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean bacteria counts among the five strains of Staphylococcus aureus? (Note: , ,.)
In one-way ANOVA,
a. list and interpret the three sums of squares.
b. state the one-way ANOVA identity and interpret its meaning with regard to partitioning the total variation among all the data.
many species of cuckoos are brood parasites. The females lay their eggs in the nests if similar bird species that then raise the young cuckoos at the expense of their own young. The question might be asked, "Do the cuckoos lay the same size eggs regardless of the size of the bird whose nest they use"? Data on the lengths, in millimeters of cuckoo eggs found in the nests of six bird species- Meadow Pipit, Tree pipit, Hedge Sparrow, Robin, Pied Wagtail and wren are provided on the WeissStats site. These data are collected by the late O. Latter in \(1902\) and used by L. Tippett in his text The Methods of Statistics.
a. Obtain individual normal probability plots and the standard deviations of the sample.
b. Perform a residual analysis
c. use your results from part (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\(5%\) significance level whether, the data provide sufficient evidence to conclude that a difference exists among the means of the populations from which the samples were taken.
e. Interpret your results from part (d).
The US Geological Survey, in cooperation with the Florida Department of Environment protection, investment the effects of waste disposal practices on ground water quality at five poultry farms in north-central Florida. At one site they drilled four monitoring wells, numbered \(1, 2, 3\) and \(4\). Over a period of \(9\) months, water samples were collected from the last three wells and analyzed for a variety of chemicals, including potassium, chlorides, nitrates and phosphorus. The concentrations in milligrams per litter are provided on the WeissStats site. For each of the four chemicals, decide whether the data provide sufficient evidence to conclude that a difference exists, in mean concentrations among the three wells. Use \(\alpha =0.01\).
we provide data from independent simple random samples from several populations. In each case,
a. compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.l on page 535
b. compare your results in part (a) for SSTR and SSE with those you obtained in Exercises 13.24-13.29, where you employed the defining formulas.
c. construct a one-way ANOVA table.
d. decide, at thesignificance level, whether the data provide sufficient evidence to conclude that the means of the populations from which the samples were drawn are not all the same.
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