Question

A sports analyst wants to determine if the number of free throws basketball players make in their second year is more than the number of free throws they make in their rookie year. To do this, he selects several random players and compares the average number of free throws they made per game in their second year of playing basketball to the average number of free throws they made per game in their rookie year. Find the test statistic and degrees of freedom for an appropriate hypothesis test using the data set below. Let the difference d for each player be computed as d=second year−rookie year. Assume that the free throws are normally distributed. Round the test statistic to three decimal places.

Rookie Year (throws per game)   Second Year (throws per game)
7.41 8.51
6.52 6.87
5.22 6.42
7.12 7.76
8.06 8.41
5.64 5.74
7.13 7.26
5.97 6.82
4.16 5.92

T =

DF=
7.63   8.46
5.32   6.04

Answer 1

Following table shows the calculations:

Second Year	Rookie year	d	(d-mean)^2
8.51	7.41	1.1	0.1369
6.87	6.52	0.35	0.1444
6.42	5.22	1.2	0.2209
7.76	7.12	0.64	0.0081
8.41	8.06	0.35	0.1444
5.74	5.64	0.1	0.3969
7.26	7.13	0.13	0.36
6.82	5.97	0.85	0.0144
5.92	4.16	1.76	1.0609
8.46	7.63	0.83	0.01
6.04	5.32	0.72	0.0001
Total		8.03	2.497

Conclusion: There is evidence to conclude that the number of free throws basketball players make in their second year is more than the number of free throws they make in their rookie year.