Archaeologists studying meat storage methods employed by the Nunamiut in northern Alaska have developed a Meat Drying Index. Following is a slightly simplified version of the index given in the article “A Zooarchaeological Signature for Meat Storage: Rethinking the Drying Utility Index”(T. Friesen, American Antiquity, 2001:315-331). Let m represent the weight of meat, b the weight of bone, and g the gross weight of some part of a caribou. The Meat Drying Index y is given by y = mb/g. Assume that for a particular caribou rib, the following measurements are made (in grams): g = 3867.4 ± 0.3, b = 1037.0 ± 0.2, m = 2650.4 ± 0.1.

a. Estimate y, and find the uncertainty in the estimate.

b. Which would provide the greatest reduction in the uncertainty in y: reducing the uncertainty in g to 0.1 g, reducing the uncertainty in b to 0.1 g, or reducing the uncertainty in m to 0?

Answer :

Step 1 of 3 :

Given,

Archaeologists studying meat storage methods employed by the Nunamiut in northern Alaska have developed a Meat drying index

Let, y = mb/g.

Where, m = weight of meat, b = weight of bone, g = gross weight of some part of a caribou

and y is the meat drying index.

We have, g = 3867.40.3 , b = 1037.00.2 and m = 2650.40.1

We have to find estimate y and uncertainty in the estimate.In reducing the uncertainty in g to 0.1g, reducing the uncertainty in b to 0.1g, or reducing the uncertainty in m to 0, in these three which would provide the greatest reduction in the uncertainty in yStep 2 of 3 :

The claim is to find the estimate of y and the uncertainty in the estimateWe have g = 3867.4, = 0.3, b = 1037.0, = 0.2, m = 2650.4 and =0.1

The estimate y =

=

= 710.6750

The estimate y = 710.6750

We have to find =

Where, =

= -

= -

= -0.1838

=

=

=

= 0.6853

And =

=

=

= 0.2687

Substitute these value in =

=

=

= 0.150

Therefore, the estimate y is 710.6750 and the uncertainty in the estimate is 0.15

Hence, y = 710.67500.15