Suppose an education administrator wants to know whether the test scores of a new standardized graduation exam are different for males and females. To test this hypothesis, the administrator decides...

Suppose an education administrator wants to know whether the test scores of a new standardized graduation exam are different for males and females. To test this hypothesis, the administrator decides to perform a ?‑test for two independent means.

She takes a random sample of test scores from both male and female populations. Some of the summary data are shown in the table.

The administrator assumes that the population variances are equal, so she computes a pooled ?‑test statistic. Determine the number of degrees of freedom, df, for the pooled ?‑statistic.