# 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.

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

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 ${s}_{1}^{2}$ and ${s}_{2}^{2}$ are the sample variances of two population with equal population variances, then "pooled variance" is given by

In this case, the test statistic for comparing means is given by

(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

and the test statistic is

(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
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 be the readings, in hours of sleep, an the i-th individual before and after the drug is givenrespectively.