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As Part of a Study of the Swimming Speed of Sharks

question 27

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As part of a study of the swimming speed of sharks, a random sample of 18 lemon sharks (Triakis semifasciata) were observed in a laboratory sea tunnel. Body lengths and maximum sustainable swimming speeds ("MSSS," reported in body lengths per second) were measured for each shark. The computer output from a regression with y = MSSS and x = body length is given below. ​
Linear Fit As part of a study of the swimming speed of sharks, a random sample of 18 lemon sharks (Triakis semifasciata)  were observed in a laboratory sea tunnel. Body lengths and maximum sustainable swimming speeds ( MSSS,  reported in body lengths per second)  were measured for each shark. The computer output from a regression with y = MSSS and x = body length is given below. ​ Linear Fit   ​ Summary of Fit RSquare 0.526395 RSquare Adj 0.496794 S 0) 272031 Mean of Response 1.24 N Observations 18 ​ Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 1 1.3159870 1.31599 17.7834 Error 16 1.1840130 0.07400 Prob > F Total 17 2.5000000 0.0007* ​ Parameter Estimates Term Estimate Std Error t Ratio Prob > |t| Intercept 1.8928955 0.167575 11.30 < 0.0001* Length(cm)  -0.010428 0.002473 -4.22 0.0007* ​ The null hypothesis is that there is no linear relationship between body length and maximum sustainable swimming rate. At the 0.05 level of significance, should the null hypothesis be rejected? Assume all the proper conditions are met for applying a linear regression analysis. ​ A) Yes B) No C) There is not enough information to tell.
Summary of Fit
RSquare 0.526395
RSquare Adj 0.496794
S 0) 272031
Mean of Response 1.24
N Observations 18

Analysis of Variance
Source DF Sum of Squares Mean Square F Ratio
Model 1 1.3159870 1.31599 17.7834
Error 16 1.1840130 0.07400 Prob > F
Total 17 2.5000000 0.0007*

Parameter Estimates
Term Estimate Std Error t Ratio Prob > |t|
Intercept 1.8928955 0.167575 11.30 < 0.0001*
Length(cm) -0.010428 0.002473 -4.22 0.0007*

The null hypothesis is that there is no linear relationship between body length and maximum sustainable swimming rate. At the 0.05 level of significance, should the null hypothesis be rejected? Assume all the proper conditions are met for applying a linear regression analysis.


Definitions:

Perceptual Studies

The examination of how organisms interpret and understand their environments through sensory input.

Lex Talionis

A principle of retributive justice meaning "the law of retaliation", where the punishment corresponds directly to the offense, as in "an eye for an eye".

Theory of Punishment

A set of principles that aim to justify and guide the imposition of penalties on individuals who violate laws, focusing on deterrence, retribution, rehabilitation, and restoration.

Retribution

A principle of justice that prescribes punishment for an offense should be proportionate to the severity of the crime committed.

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