Question

One of the greatest debates in the history of great debates: Who’s the G.O.A.T (greatest of all time): Michael Jordan or LeBron James? Although this is a highly complex question, let’s try to get at it by comparing the two on just one performance measure: average points per game (PPG). Below is a table with the average PPG per season for each Jordan and James:

SEASON	Jordan PPG	James PPG
1	28.2	20.9
2	22.7	27.2
3	37.1	31.4
4	35	27.3
5	32.5	30
6	33.6	28.4
7	31.5	29.7
8	30.1	26.7
9	32.6	27.1
10	26.9	26.8
11	30.4	27.1
12	29.6	25.3
13	28.7	25.3
14	22.9	26.4
15	20

With the above data, answer the following:

1. This is a non-traditional example that will require a t-test. However, the book only discusses the use of t-tests in terms of comparing sample means. Here, we are going to apply the t-test to two sets of data, each collected from one individual (i.e., we’re comparing multiple data points from one individual to multiple data points from another individual). With this said, which type of t-test do you believe to be most appropriate here: a related samples or independent samples? Please explain why.

2. State the appropriate alternative and null hypotheses (using the statistical notation for stating mathematical relationships) to test the hypothesis that Jordan and James will significantly differ with respects to average PPG.

3. Assuming an alpha level of 0.05, provide the critical and obtained values for this hypothesis test.

4. Assuming an alpha level of 0.05, make a decision as to whether the result of the hypothesis test is significant or insignificant, as well as whether you should reject or fail to reject the null hypothesis, being sure to explain why. Also, interpret the results of the hypothesis test in everyday language (i.e., do Jordan and James differ with respects to average PPG?).

Answer 1

	Jordan PPG ( X )		James PPG ( Y )
	28.2	1.5708	20.9	38.6175
	22.7	45.6071	27.2	0.0073
	37.1	58.472	31.4	18.3672
	35	30.7659	27.3	0.0345
	32.5	9.2824	30	8.3273
	33.6	17.1951	28.4	1.653
	31.5	4.189	29.7	6.6858
	30.1	0.4182	26.7	0.1716
	32.6	9.9017	27.1	0.0002
	26.9	6.5193	26.8	0.0988
	30.4	0.8962	27.1	0.0002
	29.6	0.0215	25.3	3.2917
	28.7	0.5675	25.3	3.2917
	22.9	42.9457	26.4	0.5102
	20	89.3649
Total	441.8	317.7173	379.6	81.057

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 1.6714
Test Criteria :-
Reject null hypothesis if


DF = 21


Result :- Fail to Reject Null Hypothesis

Conclusion :- Accept Null Hypothesis

There is no sufficient evidence to support the claim that Jordan and James will significantly differ with respects to average PPG.