Question

In: Advanced Math

a) Merchandise is sold at concerts. The manager of a concert claims that the mean value...

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%.

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