Comparing Two Means: Examples & Assumptions

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Discussion Overview

The discussion revolves around the assumptions of the 2-sample t confidence interval, specifically focusing on the equality of variances in two populations. Participants explore examples and conditions under which this assumption may not hold, as well as the implications of such failures.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that the assumption of equal variances may fail when comparing the mean heights of males and females on a campus with a predominantly Asian female population, citing potential differences in variance based on ethnicity.
  • Another participant questions the specific conditions under which the assumption is likely to fail.
  • A third participant asserts that the probability of the two variances being equal is exactly zero, implying a strong stance on the issue.

Areas of Agreement / Disagreement

The discussion reflects disagreement regarding the nature of the assumption of equal variances, with some participants questioning its validity and others asserting it as a definitive statement.

Contextual Notes

Participants express uncertainty about the appropriateness of examples and the assumptions underlying the variances in different populations.

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 height of males and females on a certain campus where females are predominantly asian. Then since variance in height of asian women is much smaller than variance in height 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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