Assume that an article in a weekend newspaper implies that more than half of all Sydney residents would prefer tolls on all motorways to be reduced by 25 cents, rather than receiving a $100 lower annual registration cost for their cars. Also assume that this was based on a poll where 562 of 1,040 participants indicated that they would rather have the reduced motorway tolls (You need to show all your calculations and demonstrate how you obtain your results).
(a) Is there evidence based on the survey data that more than half of all Sydney residents would rather have motorway tolls reduced by 25 cents than have their annual car registration lowered by $100. You should justify your answer with a hypothesis test at the 5% significance level.
(b) Calculate the p-value of your hypothesis test in Part (a) and interpret its value.