3 A transport authority wished to compare the performance of two rail companies, Western and Northern. They noted that the number of 'on-time' arrivals for a random sample of 80 Western trains over a particular route was 71 . The corresponding number for a random sample of 90 Northern trains over a similar route was 73 .

1. Test, at the \(5 \%\) significance level, whether the population proportion of on-time Western trains exceeds the population proportion of on-time Northern trains.
2. Ranjit wishes to test whether the population proportion of on-time Western trains exceeds the population proportion of on-time Northern trains by more than 0.01 . What variance estimate should she use?