You are a quality analyst with John and Sons Company. Your company manufactures

Question

You are a quality analyst with John and Sons Company. Your company manufactures fax machines, copiers, and printers that use plain paper. The CEO of the company wants the machines to handle 99.5 percent of all the paper that is used in them without the paper getting jammed. The CEO asks you to determine the thickness of paper that the machines must be able to handle to achieve this target. Make sure you include the appropriate confidence limits for the thickness of paper that the machines must be able to handle. You must use at least one data chart, one additional graphic and three additional resources (one of which may be your text book) in your presentation to support your analysis. Thickness 0.00385 0.00358 0.00372 0.00418 0.00380 0.00399 0.00424 0.00375 0.00449 0.00422 0.00407 0.00434 0.00381 0.00421 0.00397 0.00425 0.00449 0.00462 0.00467 0.00404 0.00391 0.00431 0.00398 0.00415

Explanation / Answer

Thickness of Selected Sheets of Paper Thickness You are a quality analyst with John and Sons Company. Your company manufactures fax machines, copiers, and printers that use plain paper. The CEO of the company wants the machines to handle 99.5 percent of all the paper that is used in them without the paper getting jammed. The CEO asks you to determine the thickness of paper that the machines must be able to handle to achieve this target. What are the appropriate confidence limits for the thickness of paper that the machines must be able to handle? 0.00385 0.00358 n = 24 0.00372 x-bar = 0.00410 0.00418 s = 0.00031 0.0038 ? = 0.005 0.00399 t- score 3.1040 0.00424 Standard Error = 0.00006 0.00375 Margin of Error = 0.00019 0.00449 Lower Confidence Limit = 0.00391 0.00422 Upper Confidence Limit = 0.00430 0.00407 0.00434 The machine purchased must be such that it should be able to handle paper thicknesses in the range [0.00391, 0.00430]. 0.00381 0.00421 0.00397 Memo: 0.00425 0.00449 I was given a sample of 24 sheet thicknesses from which I was asked to develop an interval of sheet thicknesses such that 99.5% of all such sheets could be properly handled by themachine without the paper getting jammed. These were the steps that I took towards meeting this objective: 0.00462 (a) I computed the mean and standard deviation of the sample of 24 sheet thicknesses 0.00467 (b) A 99.5% confidence interval translates into a 0.005 level of significance. So, ? = 0.005 0.00404 (c) Since the sample size is small, a t- score was used to calculate the interval, rather than a z- score. For ? = 0.005 and 23degrees of freedom, the t- score is 3.1040 0.00391 (d) Standard error and Margin of error were calculated using SE = s/?n and ME = t * SE 0.00431 (e) The confidence limits were calculated as [x-bar - ME, x-bar + ME] 0.00398 0.00415 I wish to conclude and propose to the Management that all future paper purchases must be inspected for thickness and ensured that the thickess lies within the interval [0.00391, 0.00430]. Thus, 99.5% of the paper will be handled properly by the machine, resulting in enhances product efficiency and saving in cost.

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