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. 124). 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. Total Catch Search Frequency Total Catch Search Frequency 9,998 18 6,535 21 7,767 14 6,695 26 8,764 4 4,891 29 9,077 18 4,937 23 8,343 9 5,727 17 9,222 5 7,019 21 6,827 8 5,735 20 2,785 35 Source: Based on G. G. Shester, “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).

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 StatCrunch. A portion of the regression printout is shown below. Find the estimates of b0 and b1 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.

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

f. Find the p-value of the test on the printout. g. Give the appropriate conclusion of the test using a = .05. h. Locate and interpret the coefficient of determination, r2 , on the printout. i. Locate and interpret the coefficient of correlation, r, on the printout. j. In part g, you conducted a test to determine that total catch (y) is negatively linearly related to search frequency (x). Which of the two statistics, r or r2 , can be used to partially support this inference? Explain. k. Locate and interpret the 95% confidence interval for E(y) when x = 25 on the printout. l. Locate and interpret the 95% prediction interval for y when x = 25 on the printout.