We know that in the population at large, the chance of having a boy or girl is roughly equal. However, it’s possible that some couples can only produce children of one sex or the other. We can investigate this by looking at large families to see if an unusually large number of them involve children of just one sex.

A British study in the 1950s looked at 70 six-child families and found that there were six of these families in which all six children were boys. The national probability of a child being a boy at that time was 0.52.

a. Design and carry out a hypothesis test to investigate the proportion of all-boy families. List any assumptions you have to make to carry out the test. Interpret your findings.

b. Does your test provide evidence that some couples can only have boys? If not, what does it provide evidence for?

c. Do you have any concerns about the assumptions you had to make? If so, say how you might address these when collecting the data.