a) Merchandise is sold at concerts. The manager of a concertclaims that the mean value of merchandise sold to premium ticketholders is more than the mean value of merchandise sold to standardticket holders. The mean value of merchandise sold to a randomsample of 60 standard ticket holders at the concert is $15 with astandard deviation of $10. The mean value of merchandise sold to arandom sample of 55 premium ticket holders at the concert is $23with 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 toassume that values of merchandise sold have normaldistributions.Give a reason for your answer.

c) A machine fills packets with almonds. The weight, in grams, ofalmonds in a packet is modelled by ?(?,?2). To check that themachine is working properly, a random sample of 10 packets isselected and unbiased estimates for ? and ?2 are ?? = 202 and ?2 =3.6
Stating your hypothesis clearly, test, at the 1% level ofsignificance, whether or not the mean weight of almonds in a packetis more than 200g.

d) In order to test ?0: ? ? 35 versus ?1: ? > 35, a randomsample of ? = 15 is obtained from a population that is normallydistributed. The sample had a standard deviation of ? = 37.4. Testthis hypothesis at the level of significance of 1%.