Question

Direction: Find the appropriate rejection region in each case. (Show your complete solution.)

1. Ha: µ > µo, α= 0.05

2. Ha: µ < µo, α= 0.05

3. A right-tailed test at 10% level of significance

4. A left-tailed test at 10% level of significance

5. A two-tailed test at 10% level of significance

Answer 1

1.$H_a: µ > \mu_o, \alpha= 0.05$

Rejection: Reject H_o if z<z_{0.05}i.e. z<1.645.

2..$H_a: µ < \mu_o, \alpha= 0.05$

Rejection: Reject $H_o \text{ if } z>z_{0.05}\text{ i.e. } z>1.645.$

3.A right-tailed test at 10% level of significance

Rejection: Reject $H_o \text{ if } z<z_{0.1}\text{ i.e. } z<1.2816$

4. A left-tailed test at 10% level of significance

Rejection: Reject $H_o \text{ if } z>z_{0.05}\text{ i.e. } z>1.2816$

5. A two-tailed test at 10% level of significance

Rejection: Reject $H_o \text{ if } z>z_{0.25} \text{ and }z<-z_{0.25} \text{ i.e. } z>1.96 \text{ and } z<-1.96.$