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Chapter 13: Q.13.3 (page 526)
What symbol is used to denote the -value having area to its right? to its right? to its right?
F-values with an area of , , and a to their right are denoted as , and , respectively.
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Consider a curve with
Find the value with an area to its right.
One-way ANOVA is a procedure for comparing the means of several populations. It is the generalization of what procedure for comparing the means of two populations?
Vitamin C (ascorbate) boosts the human immune system and is effective in preventing a variety of illnesses. In a study by E. Cameron and L. Pauling, published as the paper "Supplemental Ascorbate in the Supportive Treatment of Cancer; Reevaluation of Prolongation of Survival Times in Terminal Human Cancer", patients in advanced stages of cancer were given a vitamin C supplement. Patient were grouped according to the organ affected by cancer; stomach, bronchus, colon, ovary or breast. The study yielded the survival times, given on the WeissStats site.
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).
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.
Artificial Teeth: Wear. In a study by J. Zeng et al. three materials for making artificial teeth-Endura, Duradent, and Duracross-were tested for wear. Their results were published as the paper "In Vitro Wear Resistance of Three Types of Composite Resin Denture Teeth" (Journal of Prosthetic Dentistry, Vol. 94 . Issue 5. pp. 453-457 ). Using a machine that simulated grinding by two right first molars at 60 strokes per minute for a total of 50,000 strokes, the researchers measured the volume of material worn away, in cubic millimeters. Six pairs of teeth were tested for each material. The data on the WeissStats site are based on the results obtained by the researchers. At the 5 % significance level, do the data provide sufficient evidence to conclude that there is a difference in mean wear among the three materials?
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