Question

For the given null ( ?0 ) and alternative ( ?1 ) hypotheses, find the positive value, ? , and the negative value, −? , that define the critical region (rejection region) for a one-sample two-tailed ? ‑test for a mean with a significance level of ?=0.040 . ?0:?=5,?1:?≠5. Use software to find the values of ? to at least three decimal places. You may find one of these software manuals useful. −?= ? ?=?

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 5

H_a : $\mu$   $\neq$ 5

$\alpha$ = 0.040

$\alpha$/2 = 0.020

Z_$\alpha$/2 = Z_0.020 = 2.054

-z < -2.054 and z > 2.054