In: Advanced Math
a) Merchandise is sold at concerts. The manager of a concert
claims that the mean value of merchandise sold to premium ticket
holders is more than the mean value of merchandise sold to standard
ticket holders. The mean value of merchandise sold to a random
sample of 60 standard ticket holders at the concert is $15 with a
standard deviation of $10. The mean value of merchandise sold to a
random sample of 55 premium ticket holders at the concert is $23
with a standard deviation of $8. Test the manager’s claim at the 5%
level of significance. State your hypothesis clearly.
b) For the test in part a), state whether or not it is necessary to
assume that values of merchandise sold have normal
distributions.Give a reason for your answer.
c) A machine fills packets with almonds. The weight, in grams, of
almonds in a packet is modelled by ?(?,?2). To check that the
machine is working properly, a random sample of 10 packets is
selected and unbiased estimates for ? and ?2 are ?̅ = 202 and ?2 =
3.6
Stating your hypothesis clearly, test, at the 1% level of
significance, whether or not the mean weight of almonds in a packet
is more than 200g.
d) In order to test ?0: ? ≤ 35 versus ?1: ? > 35, a random
sample of ? = 15 is obtained from a population that is normally
distributed. The sample had a standard deviation of ? = 37.4. Test
this hypothesis at the level of significance of 1%.