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Chapter 13: Q.13.30 (page 533)
Show that, for two populations, , where is the pooled variance defined in Section 10.2 on page 407 . Conclude that is the pooled sample standard deviation, .
The standard deviation of the pool.
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In one-way ANOVA, what is the residual of an observation?
13.19 What does the term one-way signify in the phrase one-way?
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.
a. Obtain individual normal probability plots and the standard deviations 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 and the data is reasonable. If so, also do parts .
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 from which the samples were taken.
e. Interpret your results from part (d).
Weight Loss and BMI. In the paper "Voluntary Weight Reduction in Older Men Increases Hip Bone Loss: The Osteoporotic Fractures in Men Study" (Journal of Clinical Endocrinology & Metabolism, Vol. 90, Issue 4. Pp. ), K. Ensrud et al. reported on the effect of voluntary weight reduction on hip bone loss in older men. In the study, 1342 older men participated in two physical examinations an average of years apart. After the second exam, they were categorized into three groups according to their change in weight between exams: weight loss of more than , weight gain of more than , and stable weight (between loss and gain). For purposes of the hip bone density study, other characteristics were compared, one such being body mass index (BMI). On the Weissstats site, we provide the BMI data for the three groups, based on the results obtained by the researchers.
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.
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