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	51.4	50	3.6	49	0.05
b)	μ > μ0	39.7	40.1	6.2	31	0.15
c)	μ < μ0	31.8	30	8.9	33	0.10

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

Ho :   µ =   50                  
Ha :   µ ╪   50       (Two tail test)          
                          
Level of Significance ,    α =    0.05                  
population std dev ,    σ =    3.6000                  
Sample Size ,   n =    49                  
Sample Mean,    x̅ =   51.4000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   3.6000   / √    49   =   0.5143      
Z-test statistic= (x̅ - µ )/SE = (   51.400   -   50   ) /    0.5143   =   2.72
                          
critical z value, z* =   ±   1.9600   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
Decision:|test stat| > |critical|, Reject null hypothesis                       

Cohen's d=|(mean - µ )/std dev|=   0.39
MEDIUM

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

Ho :   µ =   40.1                  
Ha :   µ >   40.1       (Right tail test)          
                          
Level of Significance ,    α =    0.15                  
population std dev ,    σ =    6.2000                  
Sample Size ,   n =    31                  
Sample Mean,    x̅ =   39.7000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   6.2000   / √    31   =   1.1136      
Z-test statistic= (x̅ - µ )/SE = (   39.700   -   40.1   ) /    1.1136   =   -0.36
                          
critical z value, z* =       1.0364   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
Decision:  TEST STAT < CRITICAL VALUE , Do not reject null hypothesis

                      
Cohen's d=|(mean - µ )/std dev|=   0.06 SMALL

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

Ho :   µ =   30                  
Ha :   µ <   30       (Left tail test)          
                          
Level of Significance ,    α =    0.10                  
population std dev ,    σ =    8.9000                  
Sample Size ,   n =    33                  
Sample Mean,    x̅ =   31.8000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   8.9000   / √    33   =   1.5493      
Z-test statistic= (x̅ - µ )/SE = (   31.800   -   30   ) /    1.5493   =   1.16
                          
critical z value, z* =       -1.2816   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
Decision: |TEST STAT| < |CRITICAL | Do not reject null hypothesis           

Cohen's d=|(mean - µ )/std dev|=   0.20
SMALL

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

THANKS

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