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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

Poly(3-hydroxybutyrate) (PHB), a semicrystallinepolymer that is fully biodegradable and biocompatible,is obtained from renewable resources. From a sustainabilityperspective, PHB offers many attractive propertiesthough it is more expensive to produce than standardplastics. The accompanying data on melting point(掳C) for each of 12 specimens of the polymer using adifferential scanning calorimeter appeared in the article鈥淭he Melting Behaviour of Poly(3-Hydroxybutyrate)by DSC. Reproducibility Study鈥� (Polymer Testing,2013: 215鈥�220).

180.5 181.7 180.9 181.6 182.6 181.6

181.3 182.1 182.1 180.3 181.7 180.5

Compute the following:

  1. The sample range
  2. The sample variance \({{\bf{s}}^{\bf{2}}}\)from the definition (Hint:First subtract 180 from each observation.
  3. The sample standard deviation
  4. \({{\bf{s}}^{\bf{2}}}\)using the shortcut method

The cumulative frequency and cumulative relativefrequency for a particular class interval are the sum offrequencies and relativefrequencies, respectively, forthat interval and all intervals lying below it. If, forexample, there are four intervals with frequencies 9,16, 13, and 12, then the cumulative frequencies are 9,25, 38, and 50, and the cumulative relative frequenciesare .18, .50, .76, and 1.00. Compute the cumulativefrequencies and cumulative relative frequencies for thedata of Exercise 24.

The article 鈥淪tudy on the Life Distribution of Microdrills鈥� (J. of Engr. Manufacture, 2002: 301鈥� 305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy.

11 14 20 23 31 36 39 44 47 50

59 61 65 67 68 71 74 76 78 79

81 84 85 89 91 93 96 99 101 104

105 105 112 118 123 136 139 141 148 158

161 168 184 206 248 263 289 322 388 513

a. Why can a frequency distribution not be based on the class intervals 0鈥�50, 50鈥�100, 100鈥�150, and so on?

b. Construct a frequency distribution and histogram of the data using class boundaries 0, 50, 100, 鈥� , and then comment on interesting characteristics.

c. Construct a frequency distribution and histogram of the natural logarithms of the lifetime observations, and comment on interesting characteristics.

d. What proportion of the lifetime observations in this sample are less than 100? What proportion of the observations are at least 200?

The following data on distilled alcohol content (%) for a sample of 35 port wines was extracted from the article 鈥淎 Method for the Estimation of Alcohol in Fortified Wines Using Hydrometer Baum茅 and Refractometer Brix鈥� (Amer. J. Enol. Vitic., 2006:486鈥�490). Each value is an average of two duplicate measurements.

16.35 18.85 16.20 17.75 19.58 17.73 22.75 23.78 23.25
19.08 19.62 19.20 20.05 17.85 19.17 19.48 20.00 19.97
17.48 17.15 19.07 19.90 18.68 18.82 19.03 19.45 19.37
19.20 18.00 19.60 19.33 21.22 19.50 15.30 22.25

Use methods from this chapter, including a boxplot that
shows outliers, to describe and summarize the data.

The article 鈥淎 Thin-Film Oxygen Uptake Test for the Evaluation of Automotive Crankcase Lubricants鈥� (Lubric. Engr., 1984: 75鈥�83) reportedthe following data on oxidation-induction time (min) for various commercial oils:

87 103 130 160 180 195 132 145 211 105 145

153 152 138 87 99 93 119 129

a. Calculate the sample variance and standard deviation.

b. If the observations were re expressed in hours, what would be the resulting values of the sample variance and sample standard deviation? Answer without actually performing the re expression
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