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Chapter 2: Q167SE (page 146)

Question: If not examined carefully, the graphical description of U.S. peanut production shown at the top of the next page can be misleading.

a.Explain why the graph may mislead some readers.

b.Construct an undistorted graph of U.S. peanut production

for the given years.

Short Answer

Expert verified

Answer

  1. The graph is misleading because the graph follows a bar diagram.
  2. The distorted graph follows a multiple bar diagram.

Step by step solution

01

(a) Given the information

Given that the graphical description of U.S. peanut production shows a graph. One might distinguish the difference among categories based on statures in any layout. All classes should have identical widths. The widths and bars of creation in multiple years are distinct in the following figure, magnifying the difference among inventions in multiple years. One may now argue that the above diagram deceives certain viewers. The graph be misleading because this graph follows a bar diagram. The right way to avoid misleading the graph is if we conclude with the multiple bar diagram. Then one has to avoid misleading of the graph

02

Construct an undistorted graph

Then construct a multiple bar diagram to define the peanuts production with years. Following is an undistorted graph of U.S. peanuts production for the specified years. The graph is shown below:

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Most popular questions from this chapter

Crash tests on new cars.The National Highway Traffic Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a 鈥渟tar鈥� scoring system for the frontal crash test, with results ranging from one star (*) to five stars (). The more stars in the rating, the better the level of crash protection in a head-on collision. The NHTSA crashtest results for 98 cars (in a recent model year) are stored in the accompanying data file.

a. The driver-side star ratings for the 98 cars are summarized in the Minitab printout shown below. Use the information in the printout to form a pie chart. Interpret the graph.

Tally for Discrete Variables: DRIVSTAR

DRIVSTAR

Count

Percent

2

3

4

5

N =

4

17

59

18

98

4.08

17.35

60.20

18.37


b. One quantitative variable recorded by the NHTSA is the driver鈥檚 severity of head injury (measured on a scale from 0 to 1,500). The mean and standard deviation for the 98 driver head-injury ratings are displayed in the Minitab printout below. Give a practical interpretation of the mean.
Descriptive Statistics: DRIVHEAD

Variable

N

Mean

StDev

Minimum

Q1

Median

Q3

Maximum

DRIVHEAD

98

603.7

185.4

216.0

475.0

605.0

724.3

1240.0

C. Use the mean and standard deviation to make a statement about where most of the head-injury ratings fall.

d..Find the z-score for a driver head-injury rating of 408. Interpret the result.

Is honey a cough remedy?Refer to the Archives of Pediatrics and Adolescent Medicine(Dec. 2007) studyof honey as a remedy for coughing, Exercise 2.31 (p. 86). Recall that the 105 ill children in the sample wererandomly divided into three groups: those who receiveda dosage of over-the-counter cough medicine (DM),those who received a dosage of honey (H), and thosewho received no dosage (control group). The coughingimprovement scores (as determined by the children鈥檚parents) for the patients are reproduced in the nexttable.

Honey Dosage

12, 11, 15, 11, 10, 13, 10, 4 ,15, 16, 9, 14, 10, 6, 10, 8, 11, 12, 12, 8, 12, 9, 11, 15, 10, 15, 9, 13, 8, 12, 10, 8, 9, 5, 12

DM Dosage

4, 6, 9, 4, 7, 7, 7, 9, 12 ,10, 11, 6, 3, 4, 9, 12, 7, 6, 8, 12, 12, 4, 12, 13, 7, 10

No Dosage
(Control)

13, 9, 4, 4, 10, 15, 9, 5, 8, 6, 1, 0, 8, 12, 8, 7, 7, 1, 6, 7, 7, 12, 7, 9, 7, 9, 5, 11, 9, 5, 6, 8, 8, 6, 7, 10, 9, 4, 8, 7, 3, 1, 4, 3

a) Find the median improvement score for the honey dosage group.

b) Find the median improvement score for the DM dosage group.

c) Find the median improvement score for the control group.

d) Based on the results, parts a鈥揷, what conclusions can pediatric researchers draw? (We show how to support these conclusions with a measure of reliability in subsequent chapters.)

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: 鈥淥n average, the level of support for corporate sustainability for the 992 senior managers was 67.76 points.鈥�

b.Locate the median on the printout. Comment on the accuracy of the statement: 鈥淗alf of the 992 senior managers reported a level of support for corporate sustainability below 68 points.鈥�

c.Locate the mode on the printout. Comment on the accuracy of the statement: 鈥淢ost of the 992 senior managers reported a level of support for corporate sustainability below 64 points.鈥�

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.

Blue- vs. red-colored exam study. In a study of how external clues influence performance, university professors gave two different forms of a midterm examination to a large group of introductory students. The questions on the exam were identical and in the same order, but one exam was printed on blue paper and the other on red paper (Teaching Psychology, May 1998). Grading only the difficult questions on the exam, the researchers found that scores on the blue exam had a distribution with a mean of 53% and a standard deviation of 15%, while scores on the red exam had a distribution with a mean of 39% and a standard deviation of 12%. (Assume that both distributions are approximately mound-shaped and symmetric.)

a. Give an interpretation of the standard deviation for the students who took the blue exam.

b. Give an interpretation of the standard deviation for the students who took the red exam.

c. Suppose a student is selected at random from the group of students who participated in the study and the student鈥檚 score on the difficult questions is 20%. Which exam form is the student more likely to have taken, the blue or the red exam? Explain.

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
See all solutions

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