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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

A

No, the P-value for this test is $(2)(0.075)=0.150$ and $0.150>0.05$.

B

No, the P-value for this test is $(2)(0.03)=0.06$ and $0.06>0.05$.

C

Yes, the P-value for this test is $(\cfrac { 0.075 }{ 2 } )=0.0375$ and $0.0375<0.05$.

D

Yes the P-value for this test is $0.03$ and $0.03<0.05$.

E

Yes, the P-value for this test is $(\cfrac { 0.03 }{ 2 } )=0.015$ and $0.015<0.05$.