Question

For each of the following sets of results, compute the appropriate test statistic, test the indicated alternative hypothesis, and compute the effects size(s) indicating their magnitude:

set	Hypothesis		μ0	σ	n	α
a)	μ ≠ μ0	49	50.8	4.4	44	0.20
b)	μ > μ0	43.9	40.8	7.5	48	0.10
c)	μ < μ0	35.7	30	8.6	40	0.15

a)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =__________ ; test statistic = ________________
Decision:  ***(choose one)*** 1. Reject H0 or 2. Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d = _______________;    *(choose one)1. na 2. trivial effect 3. small effect 4. medium effect 5. large effect

b)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 or Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d ______________=  ;    *(choose one)1. na 2. trivial effect 3. small effect 4. medium effect 5. large effect

c)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =__________ ; test statistic = ________________
Decision:  ***(choose one)*** 1. Reject H0 or 2. Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d ______________=  ;    *(choose one)1. na 2. trivial effect 3. small effect 4. medium effect 5. large effect

Answer 1

a)

Standard Error , SE = σ/√n =   4.4/√44=   0.6633
Z-test statistic= (x̅ - µ )/SE =    (49-50.8)/0.6633=   -2.7136

critical z value, z* =   ±   1.2816
reject Ho

Cohen's d=|(mean - µ )/std dev|=   0.41 (medium)

b)

Standard Error , SE = σ/√n =   7.5/√48=   1.0825
Z-test statistic= (x̅ - µ )/SE =    (43.9-40.8)/1.0825=   2.8637
critical z value, z* =       1.2816

reject Ho

Cohen's d=|(mean - µ )/std dev|=   0.41 (medium)

c)

Standard Error , SE = σ/√n =   8.6/√40=   1.3598
Z-test statistic= (x̅ - µ )/SE =    (35.7-30)/1.3598=   4.1919
      
critical z value, z* =       -1.0364

fail to reject Ho

d = na