Some biologists believe the evolution of handedness is linked to complex behavio

Question

Some biologists believe the evolution of handedness is linked to complex behaviors such as tool-use. Under this theory, handedness would be genetically passed on from parents to children. That is, left-handed parents would be more likely to have left-handed children than right-handed parents. An alternate theory asserts that handedness should be random, with left- and right-handedness equally likely. In a recent study using a simple random sample of n=76 right-handed parents, 50 of the children born were right-handed. Suppose handedness is a random occurrence with either hand equally likely to be dominant, implying that the probability of a right-handed offspring is p=0.50.

Assuming left- and right-handed children are equally likely from right-handed parents, what is the probability of observing a sample proportion of at least 0.658?

Explanation / Answer

H0 null: p =0.658

H1 alternate: p >=0.658

p0 = 0.5

n = 76

p = 50/76 = 0.6579

z = (p-p0)/ sqrt[ (p0(1-po)/n ]

= (0.658-0.5)/ sqrt[ 0.5*0.5/76 ] = 2.75

P ( z>2.75) = 1 -P(z <2.75) = 1 - 0.997 = 0.003

Probability of finding a sample of atleast 0.68 is around 3%

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