Nicole and Elena wanted to know if listening to music at a louder volume negatively impacts test performance. To investigate, they recruited 30 volunteers and randomly assigned 10 volunteers to listen to music at 30 decibels, 10 volunteers to listen to music at 60 decibels, and 10 volunteers to listen to music at 90 decibels. While listening to the music, each student took a 10-question math test. Given is computer output from a least-squares regression analysis using = volume and = number correct. Predictor Coef SE Coef T P
Constant 9.9000 0.7525 13.156 0.0000
Volume –0.0483 0.0116 –4.163 0.0003
S=1.55781 R-Sq=38.2% R-Sq(adj)=36.0%

What is the -value of this test?
(Do not round)
Interpret the
P
-value of this test.

Assuming the slope of the true regression line relating
y
= performance on the 10-question math test to
x
= volume of the music is

, there is a

probability of getting a sample slope of

by chance alone.