Question

3) For a two-tailed hypothesis using a z-distribution, determine your decision (reject Ho and accept H1 OR fail to reject Ho) and the type of error you may have committed for the following situation. Be sure to draw out your distribution, indicate your critical region plus the critical values and where each of the following z-scores fall in that distribution.

a) z = -1.97 with an alpha = 0.05

b) z= +2.00 with an alpha = 0.01

c) z = + 1.50 with an alpha of 0.10

d) z = -2.99 with an alpha of 0.001

Answer 1

Ans:

a) z = -1.97 with an alpha = 0.05

critical z values=+/-1.96

Reject H₀,as z falls in rejection region

we may commit Type I error

b) z= +2.00 with an alpha = 0.01

critical z values=+/-2.576

Fail to Reject H₀,as z does not fall in rejection region

we may commit Type II error

c) z = + 1.50 with an alpha of 0.10

critical z values=+/-1.645

Fail to Reject H₀,as z does not fall in rejection region

we may commit Type II error

d) z = -2.99 with an alpha of 0.001

critical z values=+/-3.29

Fail to Reject H₀,as z does not fall in rejection region

we may commit Type II error