Provide three examples of studies when we can use (a) the pooled, (b) non-pooled, and (3) paired inference to compare means of two populations.

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Bertha Stark · Accepted Answer

In a problem of comparing means of two populations we may come across the following conditions depending on the property of data. (a)Pooled variance: when the data selected for comparing two population variance. Then we used polled variance to draw interefences and compare the means. It s12 and s22 are the sample variances of two population with equal population variances, then &quot;pooled variance&quot; is given by sp2 = (n1 − 1) s12 + (n2 − 1) s22n1 + n2 − 2 In this case, the test statistic for comparing means is given by A = x1―−x2―sp1n1+1n2 with (n1 + n2 − 2) df (b)Non - pooled variance: On the contrary the property discused in part(a) about the data, when the populations variances of two populations are assumed to be unequal, then non-pooled variance is used to compare the means of two population. It is given as S non-pooled = s12n1 + s22n2 and the test statistic is A = x1―−x2―sps12n1+s22n2‘ (c)Paired interfence(Pained test): Let us consider the case when (i) sample a sizes are equal and (ii) the samples are not independent but the sample observations are painted together. i.e. the pair of observations(x,iy.i) (i=1,2..n) comprresponding to the same i-th unit. For example. Suppose we want to test the effiency of a particular drug, say, for inducing sleep.Let xi and yi (i = 1..n) be the readings, in hours of sleep, an the i-th individual before and after the drug is givenrespectively.

Provide three examples of studies when we can use (a) the pooled, (b) non-pooled, and (3) paired inference to compare means of two populations.

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