In testing $H _ { 0 } : \rho = .80 \text { versus } H _ { \pm } : \rho

Question

In testing $H _ { 0 } : \rho = .80 \text { versus } H _ { \pm } : \rho < .80$ the rejection region for .05 level of significance test is
A) z $\geq$
1)645
B) z $\leq$
-1)645
C) -1.645 $\leq$
Z $\leq$
1)645
D) either z $\geq$
1)645 or z $\leq$
-1)645
E) z = 1.96

Quizplus · Accepted Answer

The correct answer is B because the hypothesis test is one-tailed (specifically, left-tailed) aiming to determine if $\rho$ is less than .80. For a .05 level of significance in a one-tailed test, the critical z-value is -1.645. This means the rejection region is where z is less than or equal to -1.645.

In Testing H0:ρ=.80 versus H±:ρ<.80H _ { 0 } : \rho = .80 \text { versus } H _ { \pm } : \rho < .80H0​:ρ=.80 versus H±​:ρ<.80

In Testing $H _ { 0 } : \rho = .80 \text { versus } H _ { \pm } : \rho < .80$