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Chapter 1: Q58E (page 46)

A company utilizes two different machines to manufacture parts of a certain type. During a single shift, a sample of n=20 parts produced by each machine is obtained, and the value of a particular critical dimension for each part is determined. The comparative boxplot at the bottom of this page is constructed from the resulting data. Compare and contrast the two samples.

Short Answer

Expert verified

There exists only one outlier for machine 1 and the typical values are almost the same for both the machines.

Step by step solution

01

Given information

A comparative boxplot for two different machines to manufacture parts of a certain part is provided.

02

Compare the two samples

It can be observed from the provided comparative boxplot that,

  1. The data for machine 1 is negatively skewed as compared to symmetric plot of machine 2.

2. There is only one outlier that exists for machine 1.

3. The typical value appears to be approximately the same for both machines.

4. There is more variation in the sample values of machine 2 as compared to machine 1.

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Most popular questions from this chapter

Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The article 鈥淒ust Sampling Methods for Endotoxin鈥擜n Essential, But Underestimated Issue鈥� (Indoor Air,2006: 20鈥�27) considered various issues associated with determining endotoxin concentration. The following data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the cited article.

U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0

F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0

9.2 3.0 2.0 0.3

  1. Determine the sample mean for each sample. How do they compare?
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Consider the following sample of observations on coating thickness for low-viscosity paint ("Achieving a Target Value for a Manufacturing Process: \({\rm{A}}\)Case Study, \({\rm{97}}\)J. of Quality Technology, \({\rm{1992:22 - 26}}\)):

\(\begin{array}{*{20}{r}}{{\rm{.83}}}&{{\rm{.88}}}&{{\rm{.88}}}&{{\rm{1}}{\rm{.04}}}&{{\rm{1}}{\rm{.09}}}&{{\rm{1}}{\rm{.12}}}&{{\rm{1}}{\rm{.29}}}&{{\rm{1}}{\rm{.31}}}\\{{\rm{1}}{\rm{.48}}}&{{\rm{1}}{\rm{.49}}}&{{\rm{1}}{\rm{.59}}}&{{\rm{1}}{\rm{.62}}}&{{\rm{1}}{\rm{.65}}}&{{\rm{1}}{\rm{.71}}}&{{\rm{1}}{\rm{.76}}}&{{\rm{1}}{\rm{.83}}}\end{array}\)

Assume that the distribution of counting thickness is normal (a normal probability plot strongly supports this assumption).

a. Calculate a point estimate of the mean value of coating thickness, and state which estimator you used.

b. Calculate a point estimate of the median of the coating thickness distribution, and state which estimator you used.

C. Calculate a point estimate of the value that separates the largest of\({\rm{10\% }}\) all values in the thickness distribution from the remaining \({\rm{90\% }}\)and state which estimator you used. (Hint Express what you are trying to estimate in terms of \({\rm{\mu }}\)and \({\rm{\sigma }}\)

d. Estimate \({\rm{P}}\left( {{\rm{X < 1}}{\rm{.5}}} \right){\rm{,}}\)i.e., the proportion of all thickness values less than 1.5. (Hint: If you knew the values of \({\rm{\mu }}\)and \({\rm{\sigma }}\), you could calculate this probability. These values are not available, but they can be estimated.)

e. What is the estimated standard error of the estimator that you used in part (b)?

Lengths of bus routes for any particular transit system will typically vary from one route to another. The article 鈥淧lanning of City Bus Routes鈥� (J. of the Institution of Engineers, 1995: 211鈥�215) gives the following information on lengths (km) for one particular system:

Length6-<8 8-<10 10-<12 12-<14 14-<16

Frequency6 23 30 35 32

Length16-<18 18-<20 20-<22 22-<24 24-<26

Frequency48 42 40 28 27

Length26-<28 28-<30 30-<35 35-<40 40-<45

Frequency26 14 27 11 2

a. Draw a histogram corresponding to these frequencies.

b. What proportion of these route lengths are less than 20? What proportion of these routes have lengths of at least 30?

c. Roughly what is the value of the 90th percentile of the route length distribution?

d. Roughly what is the median route length?

In 1997 a woman sued a computer keyboard manufacturer,charging that her repetitive stress injuries werecaused by the keyboard (Genessy v. Digital EquipmentCorp.).The injury awarded about \(3.5 million for painand suffering, but the court then set aside that awardas being unreasonable compensation. In making this determination, the court identified a 鈥渘ormative鈥� group of27 similar cases and specified areasonable award as onewithin two standard deviations of the mean of the awardsin the 27 cases. The 27 awards were (in \)1000s) 37, 60,75, 115, 135, 140, 149, 150, 238, 290, 340, 410, 600, 750,750, 750, 1050, 1100, 1139, 1150, 1200, 1200, 1250,1576, 1700, 1825, and 2000, from which\(\sum {{x_i} = } \)20,179,\(\sum {x_i^2} = 24,657,511\). What is the maximum possible amount that could be awarded under the two- standard deviation rule?

Mercury is a persistent and dispersive environmental contaminantfound in many ecosystems around the world.When released as an industrial by-product, it often finds itsway into aquatic systems where it can have deleteriouseffects on various avian and aquatic species. The accompanyingdata on blood mercury concentration (mg/g) for adult

females near contaminated rivers in Virginia was read from a graph in the article 鈥淢ercury Exposure Effects the Reproductive Success of a Free-Living Terrestrial Songbird, the Carolina Wren鈥� (The Auk, 2011: 759鈥�769;this is a publication of the American Ornithologists鈥� Union).

.20 .22 .25 .30 .34 .41 .55 .56

1.42 1.70 1.83 2.20 2.25 3.07 3.25

a. Determine the values of the sample mean and sample median and explain why they are different. (Hint:\(\sum {{{\bf{x}}_{\bf{1}}}{\bf{ = 18}}{\bf{.55}}} \))

b. Determine the value of the 10% trimmed mean and compare to the mean and median.

c. By how much could the observation .20 be increased without impacting the value of the sample median?
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