Single+sample+t-test+_Ch+9_ (1).pptx - The Thet ttest...

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The t–test for a single sample: an alternative to z-testThe t–test for a single sample: an alternative to z-testZ-test reminder:Compares a sample mean (M) after a treatment to the population mean (μ)Standard error describes how much difference is reasonable to expect between Mand μ within the same populationnnMM2or
z-test vs. a single sample t-testz-test vs. a single sample t-testa z-testrequires info about the population:mean, µstandard deviation, σ(to compute a standard error, σM)a single sample t-test requires info about:population mean, µBUTsamplestandard deviation (to compute an estimated standard error, sM)
Basic experimental situation for tstatistic Basic experimental situation for tstatistic The mean of population before treatment (µ) is known but not the population standard deviation (σ)
t-test uses an estimated standard errort-test uses an estimated standard errorUses sto estimate σEstimated standard error:Estimated standard error is used as estimate of the real standard error when the value of σMis unknownnsor error standard2nssestimatedM
The t-test for a single sampleThe t-test for a single sampleuses the estimated standard error, sMin place of σMMsMterrorstandardestimatedmeanpopulation-mean sample

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