Question

7.Physical Characteristics of sharks are of interest to surfers and scuba divers as well as to marine researchers. Because it is difficult to measure jaw width in living sharks, researchers would like to determine whether it is possible to estimate jaw width from body length, which is more easily measured. The following data on x = length (in feet) and y = jaw width (in inches) for 44 sharks was found in various articles appearing in the magazines Skin Diver andScuba News:

x	y		x	y		x	y		x	y
18.7	17.5		14.6	13.9		16.7	15.2		12.2	14.8
12.3	12.3		15.8	14.7		17.8	18.2		15.2	15.9
18.6	21.8		14.9	15.1		16.2	16.7		14.7	15.3
16.4	17.2		17.6	18.5		12.6	11.6		12.4	11.9
15.7	16.2		12.1	12.0		17.8	17.4		13.2	11.6
18.3	19.9		16.4	13.8		13.8	14.2		15.8	14.3
14.3	13.3		13.6	14.2		16.2	15.7		15.7	14.3
16.6	15.8		15.3	16.9		22.8	21.2		19.7	21.3
9.4	10.2		16.1	16.0		16.8	16.3		18.7	20.8
18.2	19.0		13.5	15.9		13.6	13.0		13.2	12.2
13.2	16.8		19.1	17.9		13.2	13.3		16.8	16.9

Use Minitab to answer the following questions.

e. Conduct test of H₀: B₁ = 0 vs H_a: B₁0 at a=.05.

f. Estimate the mean jaw width for sharks of length 15ft using a 95% confidence interval.

g. Assess the reasonableness of the assumptions that

Answer 1

Answer:

Physical Characteristics of sharks are of interest to surfers and scuba divers as well as to marine researchers. Because it is difficult to measure jaw width in living sharks, researchers would like to determine whether it is possible to estimate jaw width from body length, which is more easily measured. The following data on x = length (in feet) and y = jaw width (in inches) for 44 sharks was found in various articles appearing in the magazines Skin Diver andScuba News:

Use Minitab to answer the following questions.

e. Conduct test of H₀: B₁ = 0 vs H_a: B₁0 at a=.05.

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	0.69	1.30	0.53	0.599
x	0.9634	0.0823	11.71	0.000	1.00

Calculated t=0.53, P=0.599 which is > 0.05 level of significance.

Ho is not rejected.

f. Estimate the mean jaw width for sharks of length 15ft using a 95% confidence interval.

Fit	SE Fit	95% CI	95% PI
15.1396	0.212938	(14.7099, 15.5693)	(12.3302, 17.9490)

Predicted mean jaw width = 15.1396.

95% CI = (14.7099, 15.5693)

g. Assess the reasonableness of the assumptions that

Normal plot shows some deviation from straight line. Residual vs fitted plot shows some curve pattern. The residual plots shows that the assumption for regressions are violated.

MINITAB output:

Regression Analysis: y versus x

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	1	259.53	259.527	137.12	0.000
x	1	259.53	259.527	137.12	0.000
Error	42	79.49	1.893
Lack-of-Fit	31	48.43	1.562	0.55	0.904
Pure Error	11	31.06	2.823
Total	43	339.02

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
1.37574	76.55%	75.99%	74.00%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	0.69	1.30	0.53	0.599
x	0.9634	0.0823	11.71	0.000	1.00

Regression Equation

y

=

0.69 + 0.9634 x

Fits and Diagnostics for Unusual Observations

Obs	y	Fit	Resid	Std Resid
3	21.800	18.608	3.192	2.39	R
9	10.200	9.744	0.456	0.36		X
11	16.800	13.405	3.395	2.52	R
30	21.200	22.655	-1.455	-1.19		X

R Large residual
X Unusual X

Prediction for y

Regression Equation

y

=

0.69 + 0.9634 x

Settings

Variable	Setting
x	15

Prediction

Fit	SE Fit	95% CI	95% PI
15.1396	0.212938	(14.7099, 15.5693)	(12.3302, 17.9490)