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	54.4	50.4	3	30	0.20
b)	μ > μ0	43	40.5	6.5	40	0.10
c)	μ < μ0	38.8	32	9.6	34	0.01

a)
Compute the appropriate test statistic(s) to make a decision about H₀.
critical value = _______; test statistic = ____________
Decision: reject H0 or fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d = _________ ; ______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 or Fail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d =____________ ;   ---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 orFail to reject H0

Compute the corresponding effect size(s) and indicate magnitude(s).
d =___________ ;   ---Select-_____na, trivial effect, small effect, medium effect, large effect

Answer 1

a)

Ho :   µ =   50.4                  
Ha :   µ ╪   50.4       (Two tail test)          
                          
Level of Significance ,    α =    0.20                  
population std dev ,    σ =    3.0000                  
Sample Size ,   n =    30                  
Sample Mean,    x̅ =   54.4000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   3.0000   / √    30   =   0.5477      
Z-test statistic= (x̅ - µ )/SE = (   54.400   -   50.4   ) /    0.5477   =   7.30
                          
critical z value, z* =   ±   1.2816   [Excel formula =NORMSINV(α/no. of tails) ]              
                          

Decision:test stat > critical , Reject null hypothesis

Cohen's d=|(mean - µ )/std dev|=   1.33 large

..............

Ho :   µ =   40.5                  
Ha :   µ >   40.5       (Right tail test)          
                          
Level of Significance ,    α =    0.10                  
population std dev ,    σ =    6.5000                  
Sample Size ,   n =    40                  
Sample Mean,    x̅ =   43.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   6.5000   / √    40   =   1.0277      
Z-test statistic= (x̅ - µ )/SE = (   43.000   -   40.5   ) /    1.0277   =   2.43
                          
critical z value, z* =       1.2816   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
Decision:  test stat > criticcal , Reject null hypothesis                       
  

Cohen's d=|(mean - µ )/std dev|=   0.38 medium

.................

Ho :   µ =   32                  
Ha :   µ <   32       (Left tail test)          
                          
Level of Significance ,    α =    0.01                  
population std dev ,    σ =    9.6000                  
Sample Size ,   n =    34                  
Sample Mean,    x̅ =   38.8000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   9.6000   / √    34   =   1.6464      
Z-test statistic= (x̅ - µ )/SE = (   38.800   -   32   ) /    1.6464   =   4.13
                          
critical z value, z* =       -2.3263   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
Decision: |test stat| < |critical| Do not reject null hypothesis

Cohen's d=|(mean - µ )/std dev|=   0.71
medium   

.................

THANKS

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