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Chapter 16: Problem 2

Give as much information as you can about the \(P\) -value of the single-factor ANOVA \(F\) test in each of the following situations. a. \(k=5, n_{1}=n_{2}=n_{3}=n_{4}=n_{5}=4, F=5.37\) b. \(k=5, n_{1}=n_{2}=n_{3}=5, n_{4}=n_{5}=4, F=2.83\) c. \(k=3, n_{1}=4, n_{2}=5, n_{3}=6, F=5.02\) d. \(k=3, n_{1}=n_{2}=4, n_{3}=6, F=15.90\) e. \(k=4, n_{1}=n_{2}=15, n_{3}=12, n_{4}=10, F=1.75\)

Short Answer

Expert verified
The exact p-values cannot be calculated without an F-distribution table or technology, but following these steps you will be able to find the p-values for each scenario.

Step by step solution

01

Scenario a

Given \(k=5\) and all \(n_{i}=4\), we have total observations \(N=5*4=20\), degrees of freedom \(df1=k-1=5-1=4\) and \(df2=N-k=20-5=15\). With \(F=5.37\), using the F-distribution table or technology to lookup the p-value, we can find the p-value for scenario a.
02

Scenario b

Given \(k=5\), \(n_{1}=n_{2}=n_{3}=5\) and \(n_{4}=n_{5}=4\), we have total observations \(N=5*5+2*4=29\), degrees of freedom are \(df1=5-1=4\) and \(df2=29-5=24\). With \(F=2.83\), we can then find the p-value for scenario b.
03

Scenario c

Given \(k=3\), \(n_{1}=4\), \(n_{2}=5\), and \(n_{3}=6\), we have total observations \(N=4+5+6=15\), degrees of freedom are \(df1=3-1=2\) and \(df2=15-3=12\). With \(F=5.02\), we can then find the p-value for scenario c.
04

Scenario d

Given \(k=3\), \(n_{1}=n_{2}=4\), and \(n_{3}=6\), we have total observations \(N=2*4+6=14\), degrees of freedom are \(df1=3-1=2\) and \(df2=14-3=11\). With \(F=15.90\), we can then find the p-value for scenario d.
05

Scenario e

Given \(k=4\), \(n_{1}=n_{2}=15\), \(n_{3}=12\), and \(n_{4}=10\), we have total observations \(N=2*15+12+10=52\), degrees of freedom are \(df1=4-1=3\) and \(df2=52-4=48\). With \(F=1.75\), we can then find the p-value for scenario e.

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Most popular questions from this chapter

Give as much information as you can about the \(P\) -value for an upper-tailed \(F\) test in each of the following situations. a. \(\mathrm{df}_{\mathrm{l}}=4, \mathrm{df}_{2}=15, F=5.37\) b. \(\mathrm{df}_{1}=4, \mathrm{df}_{2}=15, F=1.90\) c. \(\mathrm{df}_{1}=4, \mathrm{df}_{2}=15, F=4.89\) d. \(\mathrm{df}_{1}=3, \mathrm{df}_{2}=20, F=14.48\) e. \(\mathrm{df}_{1}=3, \mathrm{df}_{2}=20, F=2.69\) f. \(\mathrm{df}_{1}=4, \mathrm{df}_{2}=50, F=3.24\)

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