n northern Europe, there are two species of flycatcher, the collared flycatcher

Question

n northern Europe, there are two species of flycatcher, the collared flycatcher and the pied flycatcher, that sometimes hybridize (i.e., a male from one species mates with a female from the other). Researchers investigated the sex of the offspring of such matings to test a pattern found in other birds - namely, that female hybrids are more likely to die before hatching than are male hybrids. The researchers found that of 26 hybrid offspring who made it to hatching, 16 were male. This compared with 72 males in 145 "purebred" offspring of matings between members of the same species. Is the proportion of males and females different in the purebred offspring than in the hybrid offspring? Do the appropriate hypothesis test.

Explanation / Answer

Let p1=16/26 =0.6153846

Let p2=72/145= 0.4965517

Ho: p1=p2

Ha: p1 not equal to p2

The test statistic is

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.6153846-0.4965517)/sqrt(0.6153846*(1-0.6153846)/26+0.4965517*(1-0.4965517)/145)

=1.14

Assume the significant level a=0.05

It is a two-tailed test.

The critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

Since Z=1.14 is between -1.96 and 1.96, we do not reject Ho.

So we can not conclude that the proportion of males and females is different in the purebred offspring than in the hybrid offspring

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