Reproduction can also be a tricky business for humans, leading to widespread adoption of assisted fertility practices such as in vitro fertilization (IVF). Each cycle of IVF might or might not lead to a pregnancy. Success rates are currently in the region of 30% per cycle for women in their late thirties.

Five women in their late thirties undergo treatment at a particular IVF clinic. The women experience respectively 3, 0, 5, 4, and 2 failed cycles before becoming pregnant on their next cycle.

a. Assume each cycle is independently successful with a constant probability p. What is a suitable model for the data given?

b. Write out an appropriate likelihood function for estimating p from these observations, and use it to find the maximum likelihood estimate of p.c. The manager of the clinic wants to check whether the clinic’s success rates are in line with the current rate of 30%. Decide upon a suitable method to investigate this question. Carry it out, and give an interpretation of your findings for the clinic manager.