5 Each person in a random sample of 1200 people was asked whether he or she approved of certain proposals to reduce atmospheric pollution. It was found that 978 people approved. The proportion of people in the whole population who would approve is denoted by \(p\).

1. Write down an estimate \(\hat { p }\) of \(p\).
2. Find a 90\% confidence interval for \(p\).
3. Explain, in the context of the question, the meaning of a \(90 \%\) confidence interval.
4. Estimate the sample size that would give a value for \(\hat { p }\) that differs from the value of \(p\) by less than 0.01 with probability \(90 \%\).