Question

A Division III college men's basketball team is interested in identifying factors thatimpact the outcomes of their games. They plan to use "point spread" (their score minustheir opponent's score) to quantify the outcome of each game this season; positive valuesindicate games that they won while negative values indicate games they lost. They wantto determine if "steal differential" (the number of steals they have in the game minus thenumber of steals their opponent had) is related to point spread; positive values indicategames where they had more steals than their opponent. The data for the first five gamesare in the provided table as an example.

Point Spread (y) Steal Differential (x)
4 7
2 -2
-21 -2
-4 1
-9 2
The correlation between point spread and steal differential for then= 25 games theyplayed this season is aboutr= 0.35. Assuming that this season was a typical season forthe team, they want to test if this sample provides evidence that steal differential ispositively correlated with point spread.

a. Define the appropriate parameter(s) and state the hypotheses for testing if this sampleprovides evidence that steal differential is positively correlated with point spread.

Answer 1

To ascertain if the steal differential is positively correlated with point spread, we state the null hypothesis H0 as no correlation and the alternative hypothesis H1 as positive correlation. A test statistic is then compared to a critical value or a p-value is used to decide whether to reject H0.

• To test if steal differential is positively correlated with point spread, the appropriate parametric hypothesis test would be a Pearson correlation test.
• The parameter of interest here is the population correlation coefficient, typically denoted as ρ (rho).
• The hypothesis statements for this test would be:

Null hypothesis (H0): ρ = 0, implying there is no correlation between steal differential and point spread.

Alternative hypothesis (H1): ρ > 0, implying there is a positive correlation between steal differential and point spread.

• The given correlation coefficient for the sample of n = 25 games is r = 0.35.
• To decide whether to reject the null hypothesis, we would typically calculate a test statistic based on this sample correlation and the sample size, and then compare it to a critical value from a statistical table, or use the p-value approach.