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	1	2	D	n	α
a)	μ1 ≠ μ2	32.7	38	4.5	24	0.10
b)	μ1 > μ2	101.3	96	9.6	26	0.01
c)	μ1 < μ2	75.2	75.4	6.8	24	0.05

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

Compute the corresponding effect size(s) and indicate magnitude(s).
d =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect
r² =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect

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

Compute the corresponding effect size(s) and indicate magnitude(s).
d =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect
r² =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect

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

Compute the corresponding effect size(s) and indicate magnitude(s).
d =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect
r² =  ; Magnitude:  ---Select--- na trivial effect small effect medium effect large effect

Answer 1

a)
Critical Value	-1.64485
Standard error =σ/√n	0.918559
Test Statistic=(x̅ - µ )/SE	-5.76991
P value	2
Decision	Fail to reject H0, fail to rejectNull hyothesis
Cohen's d=|(mean - µ )/std dev|	-1.17778
	Large

b)
Critical Value	2.326348
Standard error =σ/√n	1.882715
Test Statistic=(x̅ - µ )/SE	2.815084
P value	0.002438
Decision	Reject null hypothesis
Cohen's d=|(mean - µ )/std dev|	0.552083
	Small

c)

c)
Critical Value	-1.64485
Standard error =σ/√n	1.388044
Test Statistic=(x̅ - µ )/SE	-0.14409
P value	0.442716
Decision	Do not reject
Cohen's d=|(mean - µ )/std dev|	-0.02941
	small