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Chapter 13: Q.13.1 (page 526)
How do we identify an-distribution and its corresponding F-curve?
By stating the two degrees of freedom, an F-distribution and its matching F-curve can be determined.
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In this problem, consider an F-curve with .
Identify the degrees of freedom for the numerator.
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 section\(13.2\) we considered two hypothetical examples to explain the logic behind one-way ANOVA. Now you are to further examine those examples.
a. Refer to Table \(13.1\) on page \(528\). Perform a one-way ANOVA on the data and compare your conclusion to that stated in the corresponding "what does it mean"? box. Use \(\alpha =0.05\).
b. Repeat part (a) for the data in Table \(13.2\) on page \(528\).
Consider the following hypothetical samples
a. Obtain the sample mean and sample variance of each of the three samples.
b. Obtain SST, SSTR and SSE by using the defining formulas and verify that the one-way ANOVA identity holds.
c. Obtain SST, SSTR and SSE by using the computing formulas.
d. Construct the one-way ANOVA table.
Permeation Sampling. Permeation sampling is a method o sampling air in buildings for pollutants. It can be used over a long period of time and is not affected by humidity, air currents, or temperature. In the paper "Calibration of Permeation Passive Samplers With Silicone Membranes Based on Physicochemical Properties of the Analytes" (Analytical Chemistry, Vol. 75, No, 13, pp. 3182-3192). B. Zabiegata et al. obtained calibration constants experimentally for samples of compounds in each of four compound groups. The following data summarize their results.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean calibration constant among the four compound groups? (Note:,,)
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