Comparing Two Means: Examples & Assumptions

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The discussion focuses on the assumption of equal variances in two populations when using a 2-sample t confidence interval. A concrete example is provided, comparing the mean height of males and females on a campus where the female population is predominantly Asian, suggesting that the variance in height among Asian women is smaller than that of white males. This highlights the potential failure of the assumption of equal variances due to inherent differences in population characteristics. The conversation emphasizes that the probability of two variances being equal is effectively zero, underscoring the complexity of sampling choices. Overall, the discussion seeks to clarify when the assumption of equal variances is likely to fail in practical scenarios.
EvLer
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It's sort of a conceptual question:
one of the assumptions for 2-sample t confidence interval is equality of variances in two populations, and I need to come up with a concrete example of when this is likely to fail.
I sort of have an idea that it really depends how one chooses samples. For example, if one compares mean hight of males and females on a certain campus where females are predominantly asian. Then since variance in hight of asian women is much smaller than variance in hight of white males, the assumption fails. ALthough I am not sure if this is a good example because I make an explicit assumption that asian females have small variance in height. Could someone help me out a bit with an example?
Thanks in advance.
 
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When what is likely to fail?
 
equality of the variances of the 2 populations
 
The probability of the two variances being equal is exactly zero.
 
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