Making conclusions about slope

Leonard took a random sample of his recent text messages and found a positive linear relationship between how many minutes he took to reply and how many minutes the other person took to reply. Here is computer output from a least-squares regression analysis on his sample:

Regression: Their time vs. Leonard's time
Predictor	Coef	SE Coef	T	P
Constant	$2.915$ ‍	$0.864$ ‍	$3.376$ ‍	$0.005$ ‍
Leonard's time	$0.347$ ‍	$0.238$ ‍	$1.461$ ‍	$0.168$ ‍

Leonard wants to test

H_{0} : β = 0

vs.

H_{a} : β \neq 0

. Assume that all conditions for inference have been met.

At the $α = 0.05$ ‍ level of significance, is there sufficient evidence to conclude a linear relationship between these variables in Leonard's text messages? Why?

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 13

Problem