Consider a Study in Which We Wish to See Whether

question 44

Short Answer

Consider a study in which we wish to see whether the lengths of fish are related to the size of the lake in which they live. Unfortunately, the amount of dissolved nitrogen in the water from farm runoff is also thought to influence fish size. Imagine we are provided with the data shown in the table and wish to perform a matched design study where we compare the sizes of the fish in the largest four lakes to those in the smallest four lakes.
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$\begin{array}{cccc}\text { Fish }& \text { Fish }&\text { Lake }&\text { Dissolved }\\\underline { \text { ID \# } } &\underline { \text { size(cm) } } &\underline { \text { size } } &\underline { \text { Nitrogen } } \\1 & 25 & \text { small } & 3 \\2 & 45 & \text { small } & 21 \\3 & 28 & \text { large } & 4 \\4 & 60 & \text { large } & 15 \\5 & 35 & \text { small } & 8 \\6 & 50 & \text { large } & 20 \\7 & 33 & \text { small } & 14 \\8 & 40 & \text { large } & 7\end{array}$ ​
(a) Which fish should be in each of the two observation groups, and how should they be matched?
(b) After matching, what is the mean and standard error of the differences in the sizes of the fish?
(c) Based on your values in part (b), does there seem to be a difference in the mean size of the fish in the small and large lakes?

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Definitions:

Producer Surplus

The difference between the amount that producers are willing to accept for a good or service versus what they actually receive.

Consumer Surplus

The difference between the maximum price a consumer is willing to pay for a product and the actual market price they pay.

Government Revenue

The money received by a government from taxes, fees, fines, intergovernmental grants, and other sources to fund public spending.

Tariff

A tax imposed by a government on goods and services imported from other countries to encourage domestic consumption and protect the local industry.