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.
Losses to Robbery. The Federal Bureau of investigation conducts surveys to obtain information on the value of losses from various types of robberies. Results of the surveys are published in Population-at-Risk Rates and Selected Crime indicators, Independent simple random samples of reports for three types of robberies-highway, gas station, and convenience store gave the following data, in dollars, on the value of losses.
a. What does MSTR measure?
b. What does MSE measure?
c. Suppose that you want to perform a one-way ANOVA to compare the mean losses among the three types of robberies. What conditions are necessary? How crucial are those conditions?
Breast Milk and IQ. Considerable controversy exists over whether long-term neurodevelopment is affected by nutritional factors in early life. A. Lucas and R. Morley summarized their findings on that question for preterm babies in the publication "Breast Milk and Subsequent Intelligence Quotient in Children Born Preterm (The Lancet, Vol. 339, Issue 8788, Pp, 261-264). The researchers analyzed IQ data on children at age years. The mothers of the children in the study had chosen whether to provide their infants with breast milk within hours of delivery. The researchers used the following designations. Group I: mothers declined to provide breast milk; Group ll a: mothers had chosen but were unable to provide breast milk and Group Il b; mothers had chosen and were able to provide breast milk. Here are the summary statistics on IQ.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean IQ at age years for preterm children among the three groups? Note: For the degrees of freedom in this exercise:
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, .
For an \(F\)-curve with \(df=(20,21), find
a. \(F_{0.01}\)
b. \(F_{0.05}\)
c. \(F_{0.10}\)
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