The males of some cichlid fish species are infertile until a few days after they become the socially dominant male in the presence of females. Males without a territory (and therefore without a hope of mating) have atrophied genitalia, whereas males who control a territory with females around have well-developed genitalia. They can shift from one state to the other in a matter of days. White et al. (2002) wanted to know the hormonal signal for this shift, and one candidate hormone was gonadotropin-releasing hormone (GnRH).

They measured the levels of messenger RNA (mRNA) of GnRH for five territorial fish (T) and for six non-territorial fish (NT), in units of optical density relative to a known control. The data are in the accompanying table. Both distributions have positive skew (skewed to the right).

a. What procedure or procedures could be used to test for a difference in the mean GnRH levels between the T and NT populations?

b. Perform an appropriate hypothesis test for this difference.

c. Calculate a 95% confidence interval for the difference in GnRH mRNA level means between these two groups.

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Territorial status ΝΤΝΤ NTNT NTNT NTNT NTNT NTNT IT TT TT GnRH mRNA level 0.5040.504 0.4320.432 0.7440.744 0.7920.792 0.6720.672 1.3441.344 1.1521.152 1.2721.272 2.3282.328