Question

Hypothesis testing using Z statistics:

A researcher is interested in whether short-term memory in the elderly is different from short-term memory in the general population. The literature suggests that short-term memory declines with age.

Population mean=125                  Sample mean=121

Population SD=10                         Sample size=36

Test the hypothesis that the elderly sample has significantly less short-term memory than the general population. Use α = .05

State your z-statistic in appropriate APA format.

What is your decision?

Do you need to calculate a Cohen’s d?

t-tests:

1.       What is the critical value of t under the following conditions? (10        points)

          a. Two-tail; n=20, α=.05

          b. One-tail; n=20, α=.05

Show all work

Answer 1

Ho :   µ =   125  
Ha :   µ <   125   (Left tail test)
          
Level of Significance ,    α =    0.050  
population std dev ,    σ =    10.0000  
Sample Size ,   n =    36  
Sample Mean,    x̅ =   121.0000  
          
'   '   '  
          
Standard Error , SE = σ/√n =   10/√36=   1.6667  
Z-test statistic= (x̅ - µ )/SE =    (121-125)/1.6667=   -2.4000  
          
critical z value, z* =       -1.6449   [Excel formula =NORMSINV(α/no. of tails) ]
          
p-Value   =   0.0082   [ Excel formula =NORMSDIST(z) ]
Decision: p-value≤α, Reject null hypothesis       

Cohen's d=|(mean - µ )/std dev|=   -0.40
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1) two tail

Level of Significance ,    α =    0.05  
degree of freedom=   DF=n-1=   19  
't value='   tα/2=   2.093   [Excel formula =t.inv(α/2,df) ]

2) one tail

critical t value, t* =        1.7291