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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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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.
Rock Sparrows breeding in northern Italy are the subject of a long-term ecology and conservation study due to their wide variety of breeding patterns. Both males and females have a yellow patch on their breasts that is thought to play a significant role in their sexual behavior. A Pilastro et al. conducted an experiment in which they increased or reduced the size of a female's breast patch by dying feathers at the edge of a patch and then observed several characteristics of the behavior the male. Their results were published in the paper "Male Rock Sparrow Adjust Their Breeding Strategy According to Female Ornamentation: Parental or Mating Investment? Eight mating pairs were observed in each of three groups: a reduced patch size group, a group control and an enlarged patch size group. The data on the WeissStats site, based on the results reported by the researchers, give the number of minutes per hour that makes sang in the vicinity of the nest after the patch size manipulation was done on the females.
Starting Salaries. The National Association of Colleges and Employers (NACE) conducts surveys on salary offers to college graduates by field and degree. Results are published in Salary Survey. The following table provides summary statistics for starting salaries, in thousands of dollars, to samples of bachelor's-degree graduates in six fields.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean starting salaries among bachelor's-degree candidates in the six fields? Note; For the degrees of freedom in this exercise:
How many degrees of freedom does an -curve have? What are those degrees of freedom called?
Fill in the missing entries in the partially completed one-way ANOVA tables.
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