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Chapter 13: Q.13.2 (page 526)
How many degrees of freedom does an -curve have? What are those degrees of freedom called?
There are two degrees of freedom in the F-curve.
The numerator's first number is termed degrees of freedom, whereas the denominator's second number is called degrees of freedom.
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True or false: If you know any two of the three sums of squares, , , and , you can determine the remaining one. Explain your answer.
Magazine Ads. Advertising researchers F. Shuptrine and D. McVicker wanted to determine whether there were significant differences in the readability of magazine advertisements. Thirty magazines were classified based on their educational level-high, mid, or low - and then three magazines were randomly selected from each level. From each magazine, six advertisements were randomly chosen and examined for readability. In this particular case, readability was characterized by the numbers of words, sentences, and words of three syllables or more in each ad. The researchers published their findings in the paper "Readability Levels of Magazine Ads" (Journal of Advertising Research, Vol. 21. No. 5, pp. 45-51). The number of words of three syllables or more in each ad are provided on the WeissStats site.
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:,,)
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.
Popular Diets. In the article "Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction" (Journal of the American Medical Association, Vol. , No. 1, Pp, ), M. Dansinger et al. conducted a randomized trial to assess the effectiveness of four popular diets for weight loss. Overweight adults with an average body mass index ofand agesyears participated in the randomized trial for 1 year. The weight losses, in kilograms, based on the results of the experiment are given on the WeissStats site. Negative losses are gains. Weight Watchers.
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)
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