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Solution: Lobster fishing study. Refer to the Bulletin of
Chapter 11, Problem 81E(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). Recall that simple linear regression was used to model y = total catch of lobsters (in kilograms) during the season as a function of x = average percentage of traps allocated per day to exploring areas of unknown catch (called search frequency). A portion of the Minitab printout giving a 95% confidence interval for E(y) and a 95% prediction interval for y when x = 25 is shown below.
a. Locate and interpret the 95% confidence interval for E(y).
b. Locate and interpret the 95% prediction interval for y.
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). Recall that simple linear regression was used to model y = total catch of lobsters (in kilograms) during the season as a function of x = average percentage of traps allocated per day to exploring areas of unknown catch (called search frequency). A portion of the Minitab printout giving a 95% confidence interval for E(y) and a 95% prediction interval for y when x = 25 is shown below.
a. Locate and interpret the 95% confidence interval for E(y).
b. Locate and interpret the 95% prediction interval for y.
ANSWER:Step 1 of 2
a)
Find 95% confidence interval for .
Let response variable (y) is the total catch of lobsters and predictor variable (x) is the search frequency.
From the MINITAB output, the 95% confidence interval for is .
Interpretation:
We are 95% confident that the mean value of total catch of lobsters is between 4,783 and 6,792 when the search frequency is 25.