Does the average length of time to earn a doctorate differ from one fi­eld to another? Independent random samples from large graduate schools gave the following averages for length of registered time (in years) from bachelor’s degree to doctorate. Sample A was taken from the humanities fi­eld, and sample B from the social sciences ­field

Use a 1% level of signifi­cance to test the claim that there is no difference in the distributions of time to complete a doctorate for the two ­fields.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Compute the sample test statistic. What is the sampling distribution?

What conditions are necessary to use this distribution?

(c) Find the P-value of the sample test statistic.

(d) Conclude the test.

(e) Interpret the conclusion in the context of the application.

Transcribed Image Text:

Field A 8.9 8.3 7.2 6.4 8.0 7.5 7.1 6.0 9.2 8.7 7.5 Field B7.6 7.9 6.2 5.8 7.8 8.3 8.5 7.0 6.3 5.4 5.9 7.7