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 Standard Error (SE)

 

SE (σx) of the sample mean is σ of the dist. of sample means

  • Known pop. Var. σx= σ/ √(n)
  • Unknown pop. var sx= s/ √(n)
 
Example

25 observation are taken from a sample of unknown variance. Sample mean of 70 and
σ = 60. You wish to conduct a 2-tailed test of null hypothesis that the mean is equal to 50. What is most appropriate test statistic?

Solution

Standard Error of mean

x) = σ/ √(n) = 60/sqrt(25) = 12

Degrees of freedom = 24

Use t-statistic = (x – μ)/ σx = (70 – 50)/12 = 1.67





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