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Solved: Lobster fishing study. Refer to the Bulletin of
Chapter 11, Problem 46E(choose chapter or problem)
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 11.16 (p. 614). 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 (x).
b. Find the p-value of the test on the XLSTAT printout.
c. Give the appropriate conclusion of the test, part c, using \(\alpha=.05\).
Questions & Answers
QUESTION:
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 11.16 (p. 614). 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 (x).
b. Find the p-value of the test on the XLSTAT printout.
c. Give the appropriate conclusion of the test, part c, using \(\alpha=.05\).
ANSWER:Step 1 of 3
a)
Obtain the hypothesis for testing the negative linear relationship between total catch and search frequency as,
The null hypothesis is given below:
\({H_0}:\) The model is not negatively linearly related \(\left( {{\beta _1} = 0} \right)\).
The alternative hypothesis is given below:
\({H_a}:\) The model is negatively linearly related \(\left( {{\beta _1} < 0} \right)\).