If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means is normal if populations are non normal and the sample sizes are large.
To test hypotheses about the difference between two populations means we deal with the following three cases.
1) both the populations are normal with known standard deviations.
2)both the populations are normal with unknown standard deviations.
3) both the populations are non normal in which case both the sample sizes are necessarily large.
So, If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means is normal if populations are non normal and the sample sizes are large.
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