A company has received a shipment of 900 electric motors. The 900 electric motor

Question

A company has received a shipment of 900 electric motors. The 900 electric motors in this shipment arc packed in three shipping containers, say containers A, B, and C, with .100 motors 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 motors selected from the 300 motors in shipping container A. Each of these 50 motors will he checked to determine whether it is functioning properly. a) In this example a unit is an individual electric motor. Define (describe) an appropriate variable for the indicated objective. In other words, explain how you might test a motor and what variable you would use to indicate the outcome 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 A 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 motors is selected from the 300 motors in shipping container A. With this information in mind, what is the sampled population? In other words, describe the population which the sample of 50 motors 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. e) 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

(a) The variable that we might use to test is: whether the motor under test is functioning / not functioning (Dichotomous Nominal Variable). The values that the variable can take are: Yes and No.

(b) It may happen that all (or a majority of) the motors from one or two (but not all simultaneously) of the shipping containers are bad. In such an event, if motors from container A are found to be good, but if motors from containers B and/or C are bad, there is no way to find that out. The sample from container A can only reflect the state of motors in container A.

(c) The population is the overall group for whom the survey is being done. In this case, the population is the 300 motors in container A.

(d) The parameter is a characteristic of the entire population of 300 motors. The characteristic that is to be determined is whether the motors of the population are functioning properly. All 300 motors of the population can be checked for functioning and then we can compute the parameter = the average number out of 300 motors that are functioning properly.

(e) The statistic is a characteristic of the sample of 50 motors. All 50 motors of the randomly selected sample can be checked for functioning and then we can compute the statistic = the average number out of 50 motors that are functioning properly.

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