Question

The press release titled "Keeping Score When It Counts: Graduation Rates and Academic Progress Rates" (The Institute for Diversity and Ethics in Sport, March 16,2009 ) gave the 2009 graduation rates for African American basketball players and for white basketball players at every NCAA Division I university with a basketball program. Explain why it is not necessary to use a paired- samples \(t\) test to determine if the 2009 mean graduation rate for African American basketball players differs from the 2009 mean graduation rate for white basketball players for NCAA Division I schools.

Short answer

A paired-samples t-test is not suitable here because we're comparing two independent, unrelated groups (African American basketball players and white basketball players), not the same group under two different conditions. An independent t-test, which is designed for comparing two separate groups of independent units, would be a more appropriate choice for this scenario.

Step-by-step solution

Understanding the Paired-samples t-test

A paired-samples t-test is used to compare the means of two related groups to understand if there's a significant difference between them. The test is mainly used when the participants are subjected to two conditions and the response is to be gauged for the same group under both the conditions. The 'pairing part' comes into play because every subject experiences both conditions, and the effect of those conditions is what is compared in the end. However, in our case, the individuals in each group are distinct; African American basketball players and white basketball players are not the same individuals being compared under different conditions.

Explaining the Actual Case Requirement

In this exercise's case, we are comparing two independent groups: African American basketball players and white basketball players. These two groups didn't undergo a common condition where their responses need to be compared. Instead, we are interested in comparing the graduation rates between these two unrelated (independent) groups. Therefore, this scenario would more appropriately be suited to an independent samples t-test rather than a paired samples t-test.

Summarising the Difference in Appropriate Tests

The independent t-test is used when two separate groups of independent variables are compared, allowing the comparison of the mean graduation rate between African American basketball players and white basketball players from NCAA Division I schools. The paired t-test, on the other hand, is designed for dependent or related groups, which is not the case in our scenario. Thus, usage of a paired-samples t-test is not justifiable here, since our groups are independent.