6. A shoe shop sells on average 4 pairs of shoes per hour on a weekday morning.
- Suggest a suitable distribution for modelling the number of sales made per hour on a weekday morning and state the value of any parameters needed.
- Explain why this model might have to be modified for modelling the number of sales made per hour on a Saturday morning.
- Find the probability that on a weekday morning the shop sells
- more than 4 pairs in a one-hour period,
- no pairs in a half-hour period,
- more than 4 pairs during each hour from 9 am until noon.
The area manager visits the shop on a weekday morning, the day after an advert appears in a local paper. In a one-hour period the shop sells 7 pairs of shoes, leading the manager to believe that the advert has increased the shop’s sales.
- Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not there is evidence of an increase in sales following the appearance of the advert.
(4 marks)