Difficult# Linear Regression Slope t-test: Make It Rain Three-pointers!

APSTAT-CIEIAQ

An NBA basketball player is interested if there is an association between the amount of time a player practices his three-point shooting (in hours) and the percentage of three pointers made. Since the NBA player took AP Statistics in high school, he knew of a perfect way to design his study and share it with his NBA friends. He randomly selected $20$ NBA players and asked them how much time they spent practicing shooting behind the arc(shooting 3 pointers). He then looked up there three-point percentage. A computer output from fitting a least squares regression line to the data is shown below.

Dependent variable is: % of 3-Pointers Made

$R^2 = 91.24\%$

$S=0.052$

Variable: | Coefficient | s.e Coeff | t-ratio | prob |
---|---|---|---|---|

Constant: | 30.1 | 20 | 1.505 | .075 |

Practice Time | 0.002 | 0.000849 | 2.356 | 0.03 |

Is there sufficient evidence to suggest that there is a positive linear relationship between practice time and % of three-pointers made at the $5$% significance level? Assume the conditions for inference are met