Problem

Lobster fishing study. Refer to the Bulletin of Marine Science (April 2010) study of teams...

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.

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise. Recall that the variable of interest was the average distance separating traps—called trap spacing —deployed by teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico. The trap spacing measurements (in meters) for a sample of 7 teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap spacing measurements for 8 teams from the Punta Abreojos (PA) fishing cooperative are listed. (All these data are saved in the TRAPSPACE file). For this problem, we are interested in comparing the mean trap spacing measurements of the two fishing cooperatives.

BT Cooperative:	93	99	105	94	82	70	86
PA Cooperative:	118	94	106	72	90	66	153	98

Based on 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, pp. 479–498.

a. Identify the target parameter for this study.
b. Compute a point estimate of the target parameter.
c. What is the problem with using the normal ( z ) statistic to find a confidence interval for the target parameter?
d. Find a 90% confidence interval for the target parameter.
e. Use the interval, part d , to make a statement about the difference in mean trap spacing measurements of the two fishing cooperatives.
f. What conditions must be satisfied for the inference, part e , to be valid?

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.

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, April 2010. Reprinted with permission from the University of Miami - Bulletin of Marine Science.

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 α = .05