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Chapter 2: Q126E (page 131)

Question: Lobster trap placement.The strategic placement of lobster traps is one of the keys to a successful lobster fisherman. An observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, was conducted and the results were published in the Bulletin of Marine Science(April 2010). Two variables measured for each of eightteams from the Punta Abreojos (PA) fishing cooperativewere y= total catch of lobsters (in kilograms) during theseason and x= average percentage of traps allocated perday to exploring areas of unknown catch (called search frequency).These data are listed in the next table. Graph

the data in a scatterplot. What type of trend, if any, do you observe?

Total Catch

Search Frequency

2785

35

6535

21

6695

26

4891

29

4937

23

5727

17

7019

21

5735

20

Short Answer

Expert verified

Answer:

a. The graph is given below:


a. Downward sloping trend

Step by step solution

01

Creating the scatter plot

The graph is given below:

02

Determining the trend

When the search frequency is increased to exploring areas of unknown catch, the total catch (kg) reduces. This creates a negative relation between the total catch and the search frequency.

Therefore, there is a downward sloping trend in the data.

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Most popular questions from this chapter

Question: Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.47 (p. 96). Recall that slices of sandstone blocks were tested for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C). Measures of variation for the permeability measurements (mV) of each sandstone group are displayed in the accompanying Minitab printout.

Descriptive Statistics: PermA, PermB, PermC

Variable

N

StDev.

Variance

Minimum

Maximum

Range

PermA

100

14.48

209.53

55.20

122.40

67.20

PermB

100

21.97

482.75

50.40

150.00

99.60

PermC

100

20.05

401.94

52.20

129.00

76.80

a.Find the range of the permeability measurements for Group A sandstone slices. Verify its value using the minimum and maximum values shown on the printout.

b.Find the standard deviation of the permeability measurements for Group A sandstone slices. Verify its value using the variance shown on the printout.

c.Which condition (A, B, or C) has the more variable permeability data?

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’s 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.

Top credit card issuers, by region. The Nilson Report (December 2015) published a list of the top 150 credit card issuers worldwide. The issuers (e.g., American Express, MasterCard, Visa) were ranked based on outstanding debt during the year. The table gives a breakdown of the regions in the world served by the top 150 credit card issuers.

Worldwide Region

Number of credit
card issuers



Asia-Pacific

48


Canada

10


Europe

34


Latin America

29


Middle East/Africa

3


United States

26


Total

150


a. One of the top 150 credit card issuers is selected at random, and the region it serves is determined. What type of data (quantitative or qualitative) is measured?

b. For each region in the table, calculate the percentage of the 150 top credit card issuers that fall into that region.

c. Use the percentages, part b, to construct a relative frequency bar graph for the data summarized in the table.

d. Based on the bar graph, make a statement about the regions that most of the top 150 credit card users serve.

Construct a scattergram for the data in the following table.

Variable 1: 174 268 345 119 400 520 190 448 307 252

Variable 2: 8 10 15 7 22 31 15 20 11 9

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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