55 Lobster fishing study. The Bulletin of Marine Science (April 2010) performed a study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico. 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, saved in the TRAPSPACE file, are listed in the table.

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 accompanying SAS printout. Interpret the slope of the least squares line.

c. Give the null and alternative hypothesis 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 .

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Total Catch 2,785 6,535 6,695 4,891 4,937 5,727 7,019 5,735 Search Frequency 8888888 35 21 26 29 23 17 21 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, April 2010 (Table 1). Reprinted with permission from the University of Miami- Bulletin of Marine Science.