Previous evidence and some theory predict that the exponent describing the relationship between metabolic rate and

Previous evidence and some theory predict that the exponent β describing the relationship between metabolic rate and mass should equal 3/4. Using the data from Assignment Problem 20, test whether the exponent differs from the expected value of 3/4.

Data from Problem 20

You might think that increasing the nutrient resources available would elevate the number of plant species that an area could support, but the evidence suggests otherwise. The data in the accompanying table are from the Park Grass Experiment at Rothamsted Experimental Station in the U.K., where grassland field plots have been fertilized annually for the past 150 years (collated by Harpole and Tilman 2007). The number of plant species recorded in 10 plots is given in response to the number of different nutrient types added in the fertilizer treatment (nutrient types include nitrogen, phosphorus, potassium, and so on).

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Plot 11 22 3.3 44 55 66 77 88. 99 Number of nutrients added 00 00 00 11 22 33 11 33 44 Number of plant species 3636 3636 3232 3434 3333 3030 2020 2323 2121