**Standard Error (SE)**

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SE (Ïƒ_{x}) of the sample mean is Ïƒ of the dist. of sample means

- Known pop. Var. Ïƒ
_{x}= Ïƒ/ âˆš(n) - Unknown pop. var s
_{x}= s/ âˆš(n)

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Example

25 observation are taken from a sample of unknown variance. Sample mean of 70 and

Ïƒ = 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

(Ïƒ_{x}) = Ïƒ/ âˆš(n) = 60/sqrt(25) = 12

Degrees of freedom = 24

Use t-statistic = (x â€“ Î¼)/ Ïƒ_{x}Â = (70 â€“ 50)/12 = 1.67