A random sample of 30 pair of observations from a normal population gives a correlation coefficient of 0.32 . Is it likely that the variable in the coefficient are correlated?
"H_0:r=0" variables in the coefficient are not correlated
"H_a:r\\neq0" variables in the coefficient are correlated
"t=\\frac{r\\sqrt{n-2}}{1-r^2}=\\frac{0.32\\sqrt{30-2}}{1-0.32^2}=1.886"
"df=n-2=30-2=28"
for "\\alpha=0.05"
critical value:
"t_{crit}=2.048"
Since "|t|<t_{crit}" we accept null hypothesis. Variables in the coefficient are not correlated.
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