Lobster fishing study. Refer to the Bulletin of Marine Science (April 2010) study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 7.18 (p. 407). Two variables measured for each of 8 teams from the Punta Abreojos (PA) fishing cooperative were y = total catch of lobsters (in kilograms)

during the season and x = average percentage of traps allocated per day to exploring areas of unknown catch

(called search frequency). These data are listed in the table.

Total Catch Search Frequency 2,785 35 6,535 21 6,695 26 4,891 29 4,937 23 5,727 17 7,019 21 5,735 20 Source: From Shester, G. G. “Explaining catch variation among Baja California lobster fishers through spatial analysis of trap-placement decisions.” Bulletin of Marine Science, Vol. 86, No. 2, Apr. 2010 (Table 1).

Reprinted with permission from the University of Miami-Bulletin of Marine Science.

tRAPS

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

b. A simple linear regression analysis was conducted using SAS. Find the least squares prediction equation on the SAS printout at the bottom of the page. Interpret the slope of the least squares line.

c. Give the null and alternative hypotheses for testing whether total catch (y) is negatively linearly related to search frequency (x).

d. Find the p-value of the test, part

c, on the SAS printout.

e. Give the appropriate conclusion of the test, part

c, using a = .05.