Find the p-value for a one-way ANOVA with a test statistic [tex]$f = 6.89$[/tex], where the degrees of freedom for the error is 76 and the degrees of freedom for the groups is 5.

Question

10-12-2023
Mathematics

High School

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Find the p-value for a one-way ANOVA with a test statistic [tex]$f = 6.89$[/tex], where the degrees of freedom for the error is 76 and the degrees of freedom for the groups is 5.

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SonalG78 SonalG78 · Answer 1 · 2023-08-03T06:05:22-04:00

The p-value for a one-way ANOVA with F = 6.89, df error = 76, and df groups = 5 is smaller than 0.01, indicating strong evidence against the null hypothesis. Exact p-value requires an F-distribution table or software due to the limitations of the provided table.

To find the p-value for a one-way ANOVA given a test statistic (F = 6.89), and degrees of freedom for the error (76) and for the groups (5), one would typically use a statistical software or an F-distribution table.

However, since the table provided has only provided critical values for α = .05 and α = .01 for different degrees of freedom, and the test statistic far exceeds any of the critical values provided for 5 degrees of freedom of the numerator, we can infer that the p-value is less than 0.01. To get the exact p-value, we need the complete F-distribution data or software to assess it.

The F distribution table or software would return a probability indicating the chance of observing an F-statistic as extreme as or more extreme than our observed value, under the null hypothesis.

Given that typical significance levels are .05 and .01, and our F-statistic is considerably higher than the critical values at these levels, it's safe to conclude that the p-value would be very small, indicating strong evidence against the null hypothesis.