Question

Give as much information as you can about the \(P\) -value for an upper-tailed \(F\) test in each of the following situations. a. \(\mathrm{df}_{1}=4, \mathrm{df}_{2}=15, F=5.37\) 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. \(\mathrm{df}_{1}=4, \mathrm{df}_{2}=50, F=3.24\)

Short answer

The exact P-values can not be stated unless the F distribution table or statistical software is available. However, the main point is to understand that the P-value can be calculated given the degrees of freedom and an F value for an upper-tailed F test. This P-value tells us the probability of getting the observed data, given that the null hypothesis is true.

Step-by-step solution

Calculate the P-value for first scenario

Make use of an F distribution table, calculator, or statistical software to find the P-value for a scenario where \(\mathrm{df}_{1}=4\), \(\mathrm{df}_{2}=15\), and \(F=5.37\).

Calculate the P-value for second scenario

Determine the P-value given that \(\mathrm{df}_{1}=4\), \(\mathrm{df}_{2}=15\), and \(F=1.90\).

Calculate the P-value for third scenario

Find out the P-value for the scenario where \(\mathrm{df}_{1}=4\), \(\mathrm{df}_{2}=15\), and \(F=4.89\).

Calculate the P-value for fourth scenario

Obtain the P-value for the situation when \(\mathrm{df}_{1}=3\), \(\mathrm{df}_{2}=20\), and \(F=14.48\).

Calculate the P-value for fifth scenario

Determine the P-value for the scenario where \(\mathrm{df}_{1}=3\), \(\mathrm{df}_{2}=20\), and \(F=2.69\).

Calculate the P-value for sixth scenario

Confirm the P-value for the setting where \(\mathrm{df}_{1}=4\), \(\mathrm{df}_{2}=50\), and \(F=3.24\).