a) A courier service advertises that its average delivery time is less than six hours for local
deliveries. A random sample of the amount of time this courier takes to deliver packages
to an address across town produced the following times (rounded to the nearest hour).
7, 3, 4, 6, 10, 5, 6, 4, 3, 8
Is there sufficient evidence to support the courier’s advertisement at the 5% level of
significance?
(10 marks)
b) An inventor has developed a system that allows visitors to museums, zoos and other attractions to
get information at the touch of a digital code. For example, zoo patrons can listen to an
announcement (recorded on a microchip) about each animal they see. It is anticipated that the
device would rent for Ksh3.00 each. The installation cost for the complete system is expected to
be about Ksh 400,000. The ABC zoo is interested in having the system installed, but the
management is uncertain about whether to take the risk. A financial analysis of the problem
indicates that if more than 10% of the zoo visitors rent the system, the zoo will make a profit. To
help make the decision, a random sample of 400 zoo visitors is given details of the systems
capabilities and cost. If 48 people say that they would rent the device, can the management of the
zoo conclude at the 5% significance level that the investment would result in a profit?