Statistics 427 Assignment 4 Spring 2018 Consider a box containing a large number

Question

Statistics 427 Assignment 4 Spring 2018 Consider a box containing a large number of balls. It is known that some of the balls in the box are red and the rest are green. Suppose that a random sample of 100 balls is selected from the balls in the box and the number of red balls in the sample is determined. . The proportion of all the balls in the box that are red is a parameter . The proportion of the 100 balls in the sample that are red is a statistic. A manufacturing plant has set up two new assembly lines to allow it to compare two methods, say method A and method B, of assembling a set of four parts into a finished product. A collection of 2000 sets of the four parts is randomly divided into two groups of 1000 sets of parts. One group of parts is assembled using method A and the second group is assembled using method B The proportion of the 1000 finished products assembled using method A which pass final inspection is a statistic. . The proportion of the 1000 finished products assembled using method B which pass final inspection is a statistic. . The proportion of the entire group of 2000 finished products that would pass final inspection if all 2000 sets of parts had been assembled using method A is a parameter . The proportion of the entire group of 2000 finished products that would pass final inspection if all 2000 sets of parts had been assembled using method B is a parameter. 1. It is normal practice for a particular plastics manufacturer to provide a five year warranty on its plastic trash cans. This manufacturer has developed an accelerated life test to simulate five years of normal trash can use. The manufacturer has recently begun production of a new model of plastic trash can. A study was conducted to assess the durability of this new model of trash can. A simple random sample of 150 trash cans was selected from a batch of 6000 new model trash cans produced at a particular plant. These 150 trash cans were subjected to the simulated life test and 143 trash cans passed the test. What is a unit? What constitutes a "success" ? b) Define a suitable parameter (a proportion p). Be sure to describe the population of units this proportion corresponds to. e) Define the statistic (a proportion p) which could be used to estimate the parameter of part b)

Explanation / Answer

Part (a) : In this question, a unit is "One newly manufactured plastic trash can among the random sample of 150 new model plastic trash cans" . A "success" in this question is the event in which a plastic trash can from among the random sample of 150 new model of plastic cans, fails to pass the accelerated life test.

Part (b) : A suitable parameter is the proportion of the 6000 new model plastic trash cans which fail to pass the accelerated life test. This proportion corresponds to the population of 6000 new model plastic trash can units.

Part (c) : The statisitc which could be used to estimate the parameter of part (b) is the proportion of the 150 new model plastic trash cans which fail to pass the accelerated life tests.

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