Question

Find the rejection region (for the standardized test statistic) for each

hypothesis test.

a. H0 : μ = 27vs. Ha : μ < 27@ α = 0.05.

b. H0 : μ = 52vs. Ha : μ ≠ 52@ α = 0.05.

c. H0 : μ = −105 vs. Ha : μ > −105 @ α = 0.10.

d. H0 : μ = 78.8 vs. Ha : μ ≠ 78.8 @ α = 0.10.

Answer 1

Find the rejection region (for the standardized test statistic)

for each hypothesis test.

for this we need to use z criical value table :

## a) H0 : μ = 27 vs   Ha : μ < 27@ α = 0.05.

Answer : it is left tailed test (one tailed ) =   - 1.645

ie Z ≤ - 1.645

## b) H0 : μ = 52vs. Ha : μ ≠ 52@ α = 0.05.

Answer : it is two  tailed test =   - 1.96 to + 1.96

ie Z ≤ - 1.96 or   Z ≥  + 1.96  

## c) H0 : μ = −105 vs. Ha : μ > −105 @ α = 0.10.

Answer : it is right  tailed test (one tailed ) = 1.28

ie Z ≥  + 1.28

## d) . H0 : μ = 78.8 vs. Ha : μ ≠ 78.8 @ α = 0.10.

Answer : it is two   tailed test = - 1.645 to 1.645

ie Z ≤ - 1.645 or Z ≥  + 1.645