13.13 The largest commercial fishing enterprise in the southeastern United States is the harvest of shrimp.

In a study described in the paper “Long-term Trawl Monitoring of White Shrimp, Litopenaeus setiferus

(

Linnaeus), Stocks within the ACE Basin National Estuariene Research Reserve, South Carolina” (Journal of Coastal Research [2008]: 193–199), researchers monitored variables thought to be related to the abundance of white shrimp.

One variable the researchers thought might be related to abundance is the amount of oxygen in the water. The relationship between mean catch per tow of white shrimp and oxygen concentration was described by fitting a regression line using data from 10 randomly selected offshore sites. (The “catch per tow”

is the number of shrimp caught in a single outing.)

Computer output is shown below.

The regression equation is Mean catch per tow = 2 5859 1 97.2 O2 Saturation Predictor Coef SE Coef T P Constant 25859 2394 22.45 0.040 O2 Saturation 97.22 34.63 2.81 0.023 S 5 481.632 R-Sq 5 49.6% R2Sq(adj) 5 43.3%

a. Is there convincing evidence of a useful linear relationship between the shrimp catch per tow and oxygen concentration density? Explain. (Hint: See Example 13.5.)

b. Would you describe the relationship as strong?

Why or why not?

c. Construct a 95% confidence interval for b and interpret it in context. (Hint: See Example 13.4.)