When a park is redeveloped, it is claimed that \(70 \%\) of the local population approve of the new design. Assuming this to be true, find the probability that, in a group of 10 residents selected at random,
6 or more approve,
exactly 7 approve.
A conservation group, however, carries out a survey of 20 people, and finds that only 9 approve.
Use this information to carry out a hypothesis test on the original claim, working at the \(5 \%\) significance level. State your conclusion clearly.
If the conservationists are right, and only \(45 \%\) approve of the new park,
use a suitable approximation to the binomial distribution to estimate the probability that in a larger survey, of 500 people, less than half will approve.