Suppose that Rachel studied for the Graduate Management Admission Test (GMAT) using a well-known preparation class and was thrilled to receive a total score of 760. Her friend Eric, however, thinks...

Suppose that Rachel studied for the Graduate Management Admission Test (GMAT) using a well-known preparation class and was thrilled to receive a total score of 760. Her friend Eric, however, thinks she would have scored just as well without the class.

To test the efficacy of the class, they obtain a small but random sample of 15 test results from other students using the same class. This sample's average is 567.23 with a standard deviation of 182.05. In comparison, the national average was 550.12. Assume the population's results are normally distributed but that its standard deviation is not known.

Rachel and Eric decide to perform a two-tailed ?‑test at a significance level of ?=0.05. How many degrees of freedom should they use in their calculations?