Question 1.	

A large airline has conducted a random sample of first class business
travellers to determine how many miles they travel each year.  They
undertake a random sample of 100 first class passengers and calculate
the sample mean at 76,400 miles with a sample standard deviation of
5,250 miles.

a)	Construct a 95% confidence interval estimate of the population mean
and explain what your confidence interval means.		(1.5)

	
The airline carries out a sample of 130 first class passengers to find
out if they would be prepared to pay for an office/hotel to airport
car service.  75 out of 130 passengers sampled said they would pay
more for this service.

b)	Construct a 95% confidence interval estimate of the true population
proportion of passengers that would pay for this service.
									(1.5)

The airline wants to find out how long it takes for a travel agent to
complete an aeroplane ticket from a remote computer terminal.  They
know from last year’s data that the population of transaction times is
normally distributed, with a mean transaction time of 150 seconds, and
a standard deviation of 30 seconds.

c)	Find the probability that a future transaction will take:
	i)		185 seconds or less				(1)
	ii)	More than 195 seconds			(1)
	iii)	Between 165 and 190 seconds		(1)






The airline has hired 15 new ticket staff to use the remote computer
terminal, none of which have any previous experience.  All the new
staff take a manual dexterity test.  The mean score for the 15 new
staff is 78.3 with a standard deviation of 5.  The mean test score for
the airline’s experienced workers is 81.

d)	Test the null hypothesis that the mean score of the new staff is
different from the mean score of experience staff, at the 0.05 level
of significance.