CAIE FP2 2009 June — Question 8

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2009
SessionJune
TopicHypothesis test of a normal distribution

8 Part of a research study of identical twins who had been separated at birth involved a random sample of 9 pairs, in which one twin had been raised by the natural parents and the other by adoptive parents. The IQ scores of these twins were measured, with the following results.
Twin pair123456789
IQ of twin raised by natural parents8292115132889511283123
IQ of twin raised by adoptive parents9288115134979410788130
It may be assumed that the difference in IQ scores has a normal distribution. The mean IQ scores of separated twins raised by natural parents and by adoptive parents are denoted by \(\mu _ { N }\) and \(\mu _ { A }\) respectively. Obtain a \(90 \%\) confidence interval for \(\mu _ { N } - \mu _ { A }\). One of the researchers claimed that there was no evidence of a difference between the two population means. State, giving a reason, whether the confidence interval supports this claim.