solution

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 11.20 (p. 654). A simple linear regression model relating y = total catch of lobsters (in kilograms) and x = average percentage of traps allocated per day to exploring areas of unknown catch (called search frequency) was fit to the data in the file. A portion of the XLSTAT printout is reproduced at the bottom of the page.

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

b. Find the p-value of the test on the XLSTAT printout.

c. Give the appropriate conclusion of the test, part c, using  = .05.

Exercise 11.20

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 2.126 (p. 131). Two variables measured for each of 15 teams from two fishing cooperatives 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.

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 XLSTAT. A portion of the regression printout is shown below. Find the estimates of ₀ and ₁ on the printout.

c. If possible, give a practical interpretation of the estimate of b0. If no practical interpretation is possible, explain why.

d. If possible, give a practical interpretation of the estimate of b1 . If no practical interpretation is possible, explain why.

Exercise 2.126

Lobster trap placement. Strategic placement of lobster traps is one of the keys for 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 published in Bulletin of Marine Science (April 2010). Two variables measured for each of eight 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 next table. Graph the data in a scatterplot. What type of trend, if any, do you observe?