A shopkeeper knows, from past records, that \(15 \%\) of customers buy an item from the display next to the till. After a refurbishment of the shop, he takes a random sample of 30 customers and finds that only 1 customer has bought an item from the display next to the till.
Stating your hypotheses clearly, and using a \(5 \%\) level of significance, test whether or not there has been a change in the proportion of customers buying an item from the display next to the till.
During the refurbishment a new sandwich display was installed. Before the refurbishment \(20 \%\) of customers bought sandwiches. The shopkeeper claims that the proportion of customers buying sandwiches has now increased. He selects a random sample of 120 customers and finds that 31 of them have bought sandwiches.
Using a suitable approximation and stating your hypotheses clearly, test the shopkeeper's claim. Use a \(10 \%\) level of significance.