4 The table summarises the usual method of travelling to school for 200 randomly selected pupils from primary and secondary schools in a city.

1. Write down null and alternative hypotheses for a test to examine whether there is any association between method of travel and type of school.
2. Calculate the expected frequency for primary school bus users. Calculate also the corresponding contribution to the test statistic for the usual \(\chi ^ { 2 }\) test.
3. Given that the value of the test statistic for the usual \(\chi ^ { 2 }\) test is 42.64 , carry out the test at the \(5 \%\) level of significance, stating your conclusion clearly. The mean travel time for pupils who travel by bus is known to be 18.3 minutes. A survey is carried out to determine whether the mean travel time to school by car is different from 18.3 minutes. In the survey, 20 pupils who travel by car are selected at random. Their mean travel time is found to be 22.4 minutes.
4. Assuming that car travel times are Normally distributed with standard deviation 8.0 minutes, carry out a test at the \(10 \%\) level, stating your hypotheses and conclusion clearly.
5. Comment on the suggestion that pupils should use a bus if they want to get to school quickly.