∙A consistent estimator ofisS, the sample standard deviation. Whenwe replacewithSinsdX̄/nwe get thestandard errorofX̄:seX̄Sn∙Notice that what we call the sample standard deviation,S, is anestimator of the population standard deviation,. The standard error ofX̄is an estimator ofsdX̄/n.74
∙Now again consider testingH0:0against any of the three alternatives. (Remember, ifH1:0 then thenull is effectivelyH0:≤0; ifH1:0 the null is effectivelyH0:≥0.)∙When we replacewithSin the test statistic we getTX̄seX̄nX̄S,which is easily computed given a random sampleXi:i1,...,n.75
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