Sharks: Physical characteristics of sharks are of interest to marine researchers. Data on shark length (in feet) and jaw width (in inches) for 44 sharks were collected. The range of x values used to calculate the least-squares regression line was 9.4 to 22.8 feet. Because it is difficult to measure jaw width in living sharks, researchers would like to determine whether it is possible to accurately estimate jaw width from shark length, which is more easily measured. Regression Analysis: JawWidth versus Length The regression equation is
JawWidth = 0.688 + 0.963 Length
Predictor
Constant
Length
S = 1.37574
Coef 0.688 0.963
SE Coef 1.299 0.08228
T 0.53 11.71
P 0.599 0.000
R-Sq = 76.6%
R-Sq(adj) = 76.0%
(a) Give the number for the proportion of variability in jaw width that is explained by the linear relationship with shark length? Round your answer to 4 decimal places.
(b) Predict the jaw width of a randomly-selected 17-foot shark. Round your answer to 4 decimal places.
(c) Calculate the 95% confidence interval for β1, the slope of the population regression line. Round your answer to 4 decimal places.
(d) Provide a written interpretation of the 95% confidence interval in terms of the problem.
(e) State the appropriate hypotheses to test if there is a linear relationship between shark length and jaw width.
(f) Based on the 95% confidence interval for β1, what is the decision about the null hypothesis at the 0.05 significance level?
(g) Briefly explain how you used the 95% confidence interval to make the decision.