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Chapter 13: Q.13.13 (page 532)
Explain the reason for the word variance in the phrase analysis of variance.
Variance is just a statistical method for separating identified variance data into various elements for further analysis.
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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:
In one-way ANOVA, what is the residual of an observation?
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, .
In Exercise \(13.42-13.47\) we provide data from independent simple random samples from several populations. In each case,
a. compute SST, SSTR and SSE by using the computing formulas given in Formula \(13.1\) on page \(535\).
b. compare your results in part (a) for SSTR and SSE with those you obtained in Exercises \(13.24-13.29\) where you employed the defining formulas.
c. construct a one-way ANOVA table.
d. decide at the \(5%\) significance level, whether the data provide sufficient evidence to conclude that the means of the populations from which the samples were drawn are not all the same.
On page 539, we discussed how to use summary statistics (sample sizes, sample means, and sample standard deviations) to conduct a one-way ANOVA.
a. Verify the formula presented there for obtaining the mean of all the observations, namely,
b. Show that, if all the sample sizes are equal, then the mean of all the observations is just the mean of the sample means.
c. Explain in detail how to obtain the value of the F-statistic from the summary statistics.
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