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		n	α
a)	μ ≠ μ0	13	10.7	3.2	21	0.05
b)	μ > μ0	97.5	99.8	8	18	0.01
c)	μ < μ0	21.1	20	8.6	23	0.10

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)

Ho :   µ =   13  
Ha :   µ ╪   13   (Two tail test)
          
Level of Significance ,    α =    0.050  
population std dev ,    σ =    3.2000  
Sample Size ,   n =    21  
Sample Mean,    x̅ =   10.7000  
          
'   '   '  
          
Standard Error , SE = σ/√n =   3.2/√21=   0.6983  
Z-test statistic= (x̅ - µ )/SE =    (10.7-13)/0.6983=   -3.2937  
          
critical z value, z* =   ±   1.9600   [Excel formula =NORMSINV(α/no. of tails) ]
          
p-Value   =   0.0010   [ Excel formula =NORMSDIST(z) ]
Decision:   p-value≤α, Reject null hypothesis       
  

Cohen's d=|(mean - µ )/std dev|=   0.72 (large)
  

r² = d²/(d² + 4) =    0.11 (trivial )

b)

Ho :   µ =   97.5  
Ha :   µ >   97.5   (Right tail test)
          
Level of Significance ,    α =    0.010  
population std dev ,    σ =    8.6000  
Sample Size ,   n =    18  
Sample Mean,    x̅ =   99.8000  
          
'   '   '  
          
Standard Error , SE = σ/√n =   8.6/√18=   2.0270  
Z-test statistic= (x̅ - µ )/SE =    (99.8-97.5)/2.027=   1.1347  
          
critical z value, z* =       2.3263   [Excel formula =NORMSINV(α/no. of tails) ]
          
p-Value   =   0.1283   [ Excel formula =NORMSDIST(z) ]
Decision:   p-value>α, Do not reject null hypothesis       

d, r²= Na

c)

Ho :   µ =   21.1  
Ha :   µ <   21.1   (Left tail test)
          
Level of Significance ,    α =    0.100  
population std dev ,    σ =    8.6000  
Sample Size ,   n =    23  
Sample Mean,    x̅ =   20.0000  
          
'   '   '  
          
Standard Error , SE = σ/√n =   8.6/√23=   1.7932  
Z-test statistic= (x̅ - µ )/SE =    (20-21.1)/1.7932=   -0.6134  
          
critical z value, z* =       -1.2816   [Excel formula =NORMSINV(α/no. of tails) ]
          
p-Value   =   0.2698   [ Excel formula =NORMSDIST(z) ]
Decision:   p-value>α, Do not reject null hypothesis       

d=Na

r² =NA

please revert for doubt