# Expert Answers - You work for the Quality Assurance Department

You work for the Quality Assurance Department of a manufacturing company. Your company manufactures pencils. Machine A, Pencil Maker, is set to produce pencils of mean length 190mm with a standard deviation of 0.1mm. Machine B, Pencil Giant, produces pencils of mean length 190mm with a standard deviation of 0.2mm. Your boss believes that the machines are not producing pencils of correct length. As the Quality Assurance Officer, you must select a sample of pencils, measure the length of each pencil and use the data to determine whether your boss’ claim is true.

(Each group will be given a different dataset to work with for this project)

(a) Identify your population of interest.

(b) What sampling technique would you use to select the sample for the study? Why?

(c) use a frequency table to summarize the lengths of the pencils produced by both machines.

(d) use the frequency table to estimate the mean and median length of the pencils produced by both machines.

(e) Complete the contingency table below:

(f) use the contingency table to find the probability that a randomly selected pencil from the sample:

(i) is from Machine A and exactly 190mm;

(ii) is from Machine A, given that it is 190mm;

(iii) is from Machine A or is exactly 190mm.

(g) Test the claim that the mean length of a pencil from Machine A is not 190mm. use a = 0.10 and assume that the population is normally distributed.

(h) On the basis of your analysis, what would you tell your boss about Machine A?

(i) Another sample of 50 pencils were selected from Machine. The length and diameter of each pencil was measured and the data inputted in EXCEL. A scatter diagram was drawn using EXCEL. See the diagram below.

(j) The regression line generated by EXCEL for sample of 50 pencils is y = 0.7678x – 145.24 where y is the length of the pencil and x is the diameter. What is the expected diameter of a pencil with length 189.7mm?

(Each group will be given a different dataset to work with for this project)

(a) Identify your population of interest.

(b) What sampling technique would you use to select the sample for the study? Why?

(c) use a frequency table to summarize the lengths of the pencils produced by both machines.

(d) use the frequency table to estimate the mean and median length of the pencils produced by both machines.

(e) Complete the contingency table below:

(f) use the contingency table to find the probability that a randomly selected pencil from the sample:

(i) is from Machine A and exactly 190mm;

(ii) is from Machine A, given that it is 190mm;

(iii) is from Machine A or is exactly 190mm.

(g) Test the claim that the mean length of a pencil from Machine A is not 190mm. use a = 0.10 and assume that the population is normally distributed.

(h) On the basis of your analysis, what would you tell your boss about Machine A?

(i) Another sample of 50 pencils were selected from Machine. The length and diameter of each pencil was measured and the data inputted in EXCEL. A scatter diagram was drawn using EXCEL. See the diagram below.

(j) The regression line generated by EXCEL for sample of 50 pencils is y = 0.7678x – 145.24 where y is the length of the pencil and x is the diameter. What is the expected diameter of a pencil with length 189.7mm?

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