The table shows the ages for a random sample of doctorate recipients in three fields of study. At \(\alpha=0.01\), can you conclude that the distribution of the ages of the doctorate recipients in at least one field of study is different from the others?

Use the Kruskal-Wallis test to test the claim by doing the following.

(a) Identify the claim and state \(H_{0}\) and \(H_{a}\).

(b) Find the critical value and identify the rejection region.

(c) Find the test statistic \(H\).

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

Transcribed Image Text:

Field of study Age Life sciences 31 32 34 31 30 32 35 31 32 34 29 Physical sciences 30 31 32 31 30 29 31 30 32 33 30 Social sciences 32 35 31 33 34 31 35 36 32 30 33