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I answered these homework questions but I was told that at least one of my answers is wrong. However, I can't tell which one I answered wrong. What incorrect assumptions have I made?

QUESTION:

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MY ANSWERS:

3a) Welch's T-test would be most appropriate since we have normal data with unequal variances.

3b) A Wilcoxon-Mann Whitney U Test appears to be the best option since transformations have failed and we must now use a non-parametric test for these 2 independent samples.

3c) The data has unequal variances and is not normal so we should also use a Wilcoxon-Mann Whitney U Test here too.

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  • $\begingroup$ In (c), consider the interpretation of "p-values > $\alpha$" (not that I agree with the reasoning behind these questions). $\endgroup$ – mark999 Nov 16 '16 at 5:23
  • $\begingroup$ I believe I did. When p > α in Levene's test, there are unequal variances. When p > α in the Shapiro-Wilk test, the distribution is not normal. Or am I incorrect? $\endgroup$ – orangebull Nov 16 '16 at 5:35
  • $\begingroup$ en.wikipedia.org/wiki/Levene%27s_test $\endgroup$ – mark999 Nov 16 '16 at 5:39
  • $\begingroup$ If they really will not tell you which one is wrong you might consider changing course and asking for your money back. $\endgroup$ – mdewey Nov 16 '16 at 12:25
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I have a number of issues with this question, but leaving those aside, it's clear that your answer to (c) is not what they're seeking.

When the p-value is large the null should not be rejected. In significance testing, the null hypothesis is rejected when the p-value is smaller than the significance level ($\alpha$).

It would probably be a good idea to review your understanding of the basics of hypothesis testing.

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  • $\begingroup$ I just noticed my mistakes. The variances are equal and the distribution is normal. But does that mean that an independent t-test would work best or would a correlation/regression test be more appropriate since we are working with 2 quantitative variables? $\endgroup$ – orangebull Nov 16 '16 at 17:16
  • $\begingroup$ Failing to reject the nulls doesn't tell us that the variances are actually equal or that the distribution is actually normal. You're working with the variables wing-length and species; you can do equivalent analyses either with a t-test or regression. $\endgroup$ – Glen_b Nov 16 '16 at 23:00

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