For mammals metabolic rate is related to body mass One versi

For mammals, metabolic rate is related to body mass. One version of metabolic theory (theory A) states that resting metabolic rate is proportional to an animal’s mass raised to the ¾ power. If this theory is true, then the slope of a regression line relating the logarithm of metabolic rate to the logarithm of mass should be 0.750. Another theory (theory B) states that resting metabolic rate is proportional to an animal’s mass raised to the 2/3 power. If this theory is true, then the slope of a regression line relating the logarithm of metabolic rate to the logarithm of mass should be 0.666. Researchers who were in favor of theory A did just such a regression analysis. Based on a sample of 10 mammals of different sizes (n=10), they conducted a regression analysis and estimated the slope to be 0.72 with a standard error of 0.02. This gives a 95% confidence interval of 0.674 – 0.766. Satisfied with themselves, they patted each other on the back and concluded that because 0.75 is in the interval and 0.666 is not, they can be 95% confident that theory A is correct and 95% confident that theory B is incorrect.

Solution

The sample size is very small -10

and randomness is not assured

Hence simply depending on a sample size of 10 from a particular region the conclusion may be misleading.