6 An anthropologist was studying the inhabitants of two islands, Raloa and Tangi. Part of the study involved the incidence of blood group type A. The blood of 80 randomly chosen inhabitants of Raloa and 85 randomly chosen inhabitants of Tangi was tested. The number of inhabitants with type A blood was 28 for the Raloa sample and 46 for the Tangi sample. The anthropologist calculated \(90 \%\) confidence intervals for the population proportions of inhabitants with type A blood. They were \(( 0.262,0.438 )\) for Raloa and \(( 0.452,0.630 )\) for Tangi, where each figure is correct to 3 decimal places. It is known that \(43 \%\) of the world's population have type A blood.
- State, giving your reasons, whether there is evidence for the following assertions about the proportions of people with type A blood.
(a) The proportion in Raloa is different from the world proportion.
(b) The proportion in Tangi is different from the world proportion. - Carry out a suitable test, at the \(2 \%\) significance level, of whether the proportions of people with type A blood differ on the two islands.