Statistics 427 Assignment 3 Spring 2018 A company has received a shipment of 900

Question

Statistics 427 Assignment 3 Spring 2018 A company has received a shipment of 900 high efficiency household washing machines. The 900 washing machines in this shipment are packed in three shipping containers, say containers A, B, and C, with 300 washing machines in each container. The company needs to decide whether it should keep this shipment or refuse it. They decide to make their decision about accepting or refusing the entire shipment by examining a simple random sample of 50 washing machines selected from the 300 washing machines in shipping con- tainer C. Each of these 50 washing machines will be checked to determine whether it is functioning properly a) In this example a unit is an individual washing machine. Define (describe) an ap- propriate variable for the indicated objective. That is, explain how you might test a high efficiency household washing machine and what variable you would use to indicate the out- come of the test. Be specific (explain exactly how to determine the value of the variable) and indicate the possible values of the variable. b) Briefly discuss why basing the decision regarding the acceptability of the entire shipment on this simple random sample from shipping container C is not a good idea. (Notice that this is not a question about the size of the sample.) c) Recall that the simple random sample of 50 washing machines is selected from the 300 washing machines in shipping container C. With this information in mind, what is th sampled population? That is, describe the population which the sample of 50 washing machines provides information about. d) Define (describe) an appropriate parameter for the sampled population. Define this in words, since there is not enough information to give an actual value. In other words, describe the parameter and how you would compute the value of the parameter if you had access to all of the units in the sampled population. Define (describe) an appropriate statistic. Again define this in words, since there is not enough information to give an actual value. In other words, describe the statistic and how you would compute the value of the statistic once you had access to the units in the sample.

Explanation / Answer

Here 900 washing machines are submitted in a shipment that has three container viz. A, B and C each with 300 washing machines. In this example a sample of 50 washing machines is drawn randomly from container C and decision of acceptance or rejection is taken about the shipment as a whole.

Define a random variable X : Status of a sampled washing machine. Here X may have two status either properly function or not functioning properly.

Let us denote :

Properly functioning machine = 1

Improperly functioning machine = 0

Therefore, here random variable is categorical and hence it will follow Bernoulli distribution with p = Probability that a machine functions properly =P[X=1] and 1-p=q=P[X=0]

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