Question

3. A sample is selected from a population with j = 300 After a treatment is administered to the individuals, t sample mean is found to be M = 280 and the variance is $2 = 100 (S = 10). If the sample has n = 16 scores, the calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two tailed test with a =.05.

Answer 1

Ho :   µ =   300  
Ha :   µ ╪   300   (Two tail test)
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    10.0000  
Sample Size ,   n =    16  
Sample Mean,    x̅ =   280.0000  
          
degree of freedom=   DF=n-1=   15  
          
Standard Error , SE = s/√n =   10/√16=   2.5000  
t-test statistic= (x̅ - µ )/SE =    (280-300)/2.5=   -8.000  
          
          
p-Value   =   0.0000   [Excel formula =t.dist(t-stat,df) ]
Decision:   p-value≤α, Reject null hypothesis       

so, treatment has a significant effect

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

Please let me know in case of any doubt.

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