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Chapter 2: Q124E (page 131)

Question: Repair and replacement costs of water pipes.Pipes used in a water distribution network are susceptible to breakage due to a variety of factors. When pipes break, engineers must decide whether to repair or replace the broken pipe.

A team of civil engineers estimated the ratio of repair to replacement cost of commercial pipe based on the diameter (in millimeters) of the pipe. (IHS Journal of Hydraulic Engineering,September 2012.) Data for a sample of 13 different pipe sizes are provided in the table. Use a scatterplot to aid the engineers in detecting a trend in the data. Does it appear that the ratio of repair to replacement cost is strongly associated with pipe size?

DIAMETER

RATIO

80

6.58

100

6.97

125

7.39

150

7.61

200

7.78

250

7.92

300

8.20

350

8.42

400

8.60

450

8.97

500

9.31

600

9.47

700

9.72

Short Answer

Expert verified

Answer:

The graph is given below:

Yes, the ratio of repair to replacement cost is strongly associated with pipe size.

Step by step solution

01

Constructing the scatterplot

The graph is given below:

02

Determining the trend and the association between the data

There is a positive trend in the data set. It means that the ratio of repair to replacement cost is positively related to the size of the pipe. As the size of the pipe goes on increasing, the ratio of repair to replacement cost also increases.

Therefore, yes, there is a strong association between the ratio of repair to replacement and the size of the pipe.

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Most popular questions from this chapter

Calculate the mode, mean, and median of the following data:

18 10 15 13 17 15 12 15 18 16 11

Corporate sustainability of CPA firms.Refer to the Business and Society(March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23 ( p. 83). Recall that level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each of 992 senior managers at CPA firms. Numerical measures of central tendency for level of support are shown in the accompanying Minitab printout.

Descriptive Statistics: Support

Variable

Support

N

Mean

Minimum

Median

Maximum

Mode

N for mode

992

67.755

0.000

68.000

155.000

64

20

a.Locate the mean on the printout. Comment on the accuracy of the statement: “On average, the level of support for corporate sustainability for the 992 senior managers was 67.76 points.”

b.Locate the median on the printout. Comment on the accuracy of the statement: “Half of the 992 senior managers reported a level of support for corporate sustainability below 68 points.”

c.Locate the mode on the printout. Comment on the accuracy of the statement: “Most of the 992 senior managers reported a level of support for corporate sustainability below 64 points.”

d.Based on the values of the measures of central tendency, make a statement about the type of skewness (if any) that exists in the distribution of 992 support levels. Check your answer by examining the histogram shown in Exercise 2.23.

Improving SAT scores.The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S. students from eighth grade through high school and college. Research published in Chance (Winter 2001) examined the Standardized Assessment Test (SAT) scores of 265 NELS students who paid a private tutor to help them improve their scores. The table summarizes the changes in both the SAT–Mathematics and SAT–Verbal scores for these students.

SAT–Math

SAT–Verbal

Mean change in score

19

7

Standard deviation of score changes

65

49

a.Suppose one of the 265 students who paid a private tutor is selected at random. Give an interval that is likely to contain this student’s change in the SAT–Math score.

b.Repeat part afor the SAT–Verbal score.

c.Suppose the selected student increased his score on one of the SAT tests by 140 points. Which test, the SAT– Math or SAT–Verbal, is the one most likely to have the 140-point increase? Explain.

Defects in new automobiles.Consider the following data from the automobile industry. All cars produced on a particular day were inspected for defects. The 145 defects found were categorized by type as shown in the accompanying table.

Defect Type

Number

Accessories

Body

Electrical

Engine

Transmission

50

70

10

5

10

a.Construct a Pareto diagram for the data. Use the graph to identify the most frequently observed type of defect.

b.All 70 car body defects were further classified as to type. The frequencies are provided in the following table. Form a Pareto diagram for the type of body defect. (Adding this graph to the original Pareto diagram of part a is called exploding the Pareto diagram.) Interpret the result. What type of body defect should be targeted for special attention?

Body Defect

Number

Chrome

Dents

Paint

Upholstery

Windshield

2

25

30

10

3

Voltage sags and swells.Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by“sags” and “swells”) in Turkish transformers, Exercise 2.96(p. 116). For a sample of 103 transformers built for heavyindustry, the mean and standard deviation of the numberof sags per week were 353 and 30, respectively; also, themean and standard deviation of the number of swells perweek were 184 and 25, respectively. Consider a transformerthat has 400 sags and 100 swells in a week.

a.Would you consider 400 sags per week unusual, statistically? Explain.

b.Would you consider 100 swells per week unusual, statistically? Explain.
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