A shop sells shoes at a mean rate of 4 pairs of shoes per hour on a weekday.
Suggest a suitable distribution for modelling the number of sales of pairs of shoes made per hour on a weekday.
State one assumption necessary for this distribution to be a suitable model of this situation.
Find the probability that on a weekday the shop sells
more than 4 pairs of shoes in a one-hour period,
more than 4 pairs of shoes in each of 3 consecutive one-hour periods.
The area manager visits the shop on a weekday, the day after an advert for the shop appears in a local paper.
In a one-hour period during the manager's visit, the shop sells 7 pairs of shoes. This leads the manager to believe that the advert has increased the shop's sales of pairs of shoes.
Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not there is evidence of an increase in sales of pairs of shoes following the appearance of the advert.