Hypothesis Tests for Correlation Coefficient Using TI-84 Practice 1
An economist wonders if the inflation rate is linearly correlated with the unemployment rate and is looking to use the results of their analysis for further study. They take a random sample of recent months and record the unemployment rate and inflation rate. They find $r=0.23$ and run a hypothesis test, getting a $P-value$ of $0.35$. Interpret the value of $r$ and results of the test.

$r=0.23$ suggests weak positive linear correlation; fail to reject $H_0(p=0)$ since not enough evidence to support nonzero linear correlation between inflation and unemployment.

$r=0.23$ suggests weak positive linear correlation; reject $H_0\left(p=0\right)$ since there is enough evidence to support nonzero linear correlation between inflation and unemployment.

$r=0.23$ suggests strong positive linear correlation; fail to reject $H_0\left(p=0\right)$ since not enough evidence to support nonzero linear correlation between inflation and unemployment.

$r=0.23$ suggests strong positive linear correlation; reject $H_0\left(p=0\right)$ since there is enough evidence to support nonzero linear correlation between inflation and unemployment.