17 Flies like almost all other living organisms have builtin

17. Flies, like almost all other living organisms, have built-in circadian rhythms that keep time even in the absence of external stimuli. Several genes have been shown to be involved in internal time-keeping. including per (period) and rim (timeless). Mutations in these two genes. and in other genes, disrupt time-keeping abilities. Interestingly, these genes have also been shown to be involved in other time-related behavior, such as the frequency of wing beats in male courtship behaviors. Individuals that carry mutations of per and tim have been shown to copulate for longer than individuals that have neither mutation. But do these two mutations affect copulation time in similar ways? The following table summarizes some data on the duration of copulation for flies that carry either the tim mutation or the per mutation (Beaver and Giebultowicz 2004): a. Do these two mutations have different mean copulation durations? Carry out the appropriate test. b. Do the populations carrying these mutations have different variances in copulation duration?

Solution

Answer to part a)

We need to do a T test for mean difference of independent samples

The formula of test statistic is:

t = (x1 bar - x2bar) / sqrt[ s1^2 / n1 + s2^2 / n2]

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On plugging the values we get:

t = (17.5 -19.9) / sqrt(3.37^2/14 + 2.47^2/17)

t = -2.22

df = n1+n2 - 2

df = 14+17 -2

df = 29

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P value will can be found using the following formula in excel:

=T.DIST.2T(2.22,29)

We get P value = 0.0344

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Inference:

Since the P value < 0.05 , we reject the null

Conclusion: The two means are different

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Answer to part b)

We conduct a F test to conduct hypothesis test of two variances

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F = s1^2 / s2^2

F = 3.37^2 / 2.47^2

F = 1.8615

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df 1 = (14-1) = 13

df 2 = (17 -1 ) = 16

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Thus the P value for this F value can be found using the following excel formula:

=1-F.DIST(1.8615,13,16,1)

We get P value = 0.11937

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Inference:

Since the P value > 0.05 , we fail to reject the null

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Conclusion: Thus we conlcude that the two variances are equal