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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

A mutual fund is a professionally managed investment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of investments, whereas blended funds seek a balance between current income and growth. Here is data on the expense ratio (expenses as a % of assets, from www .morningstar.com) for samples of 20 large-cap balanced

funds and 20 large-cap growth funds (鈥渓argecap鈥� refers to the sizes of companies in which the funds invest; the population sizes are 825 and 762,

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Bl 1.03 1.23 1.10 1.64 1.30

1.27 1.25 0.78 1.05 0.64

0.94 2.86 1.05 0.75 0.09

0.79 1.61 1.26 0.93 0.84

Gr 0.52 1.06 1.26 2.17 1.55

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0.91 0.79 1.39 0.62 1.52

1.02 1.10 1.78 1.01 1.15

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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

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

Let \({{\rm{X}}_{\rm{1}}}{\rm{,}}{{\rm{X}}_{\rm{2}}}.....{\rm{,}}{{\rm{X}}_{\rm{n}}}\) represent a random sample from the Rayleigh distribution with density function given in Exercise \({\rm{15}}\). Determine a. The maximum likelihood estimator of \({\rm{\theta }}\), and then calculate the estimate for the vibratory stress data given in that exercise. Is this estimator the same as the unbiased estimator suggested in Exercise \({\rm{15}}\)? b. The mle of the median of the vibratory stress distribution. (Hint: First express the median in terms of \({\rm{\theta }}\).)

Grip is applied to produce normal surface forces that compress the object being gripped. Examples include two people shaking hands, or a nurse squeezing a patient鈥檚 forearm to stop bleeding. The article 鈥淚nvestigation of Grip Force, Normal Force, Contact Area, Hand Size, and Handle Size for Cylindrical Handles鈥� (Human Factors, 2008: 734鈥�744) included the following data on grip strength (N) for a sample of 42

individuals:

16 18 18 26 33 41 54 56 66 68 87 91 95

98 106 109 111 118 127 127 135 145 147 149 151 168

172 183 189 190 200 210 220 229 230 233 238 244 259

294 329 403

a. Construct a stem-and-leaf display based on repeating each stem value twice, and comment on interesting features.

b. Determine the values of the fourths and the fourth spread.

c. Construct a boxplot based on the five-number summary, and comment on its features.

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