A Village Has Five Residents,each of Whom Has Accumulated Savings

question 28

Multiple Choice

A village has five residents,each of whom has accumulated savings of $50.Each villager can use the money to buy a government bond that pays 10% interest per year or to buy a year-old goat,send it onto the commons to graze,and sell it after one year.The price of the goat that the villager will get at the end of the year depends on the amount of weight it gains while grazing on the commons,which in turn depends on the number of goats sent onto the commons,as shown in table below. $$\begin{array} { c c c } \begin{array} { c } \text { Number of goats } \\\text { on the commons }\end{array} & \begin{array} { c } \text { Price per 2-year-old } \\\text { goat (\$) }\end{array} & \begin{array} { c } \text { Income per goat } \\\text { (\$/year) }\end{array} \\1 & 80 & 30 \\2 & 75 & 25 \\3 & 70 & 20 \\4 & 65 & 15 \\5 & 55 & 5\end{array}$$
Refer to the information given above.Left to private incentives,the villagers earn _____ than when goat grazing is determined collectively.

• A)less total income
• B)more total income
• C)the same amount of total income
• D)either more or less total income depending on the market price of goats

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Definitions:

Significance Level

A threshold in hypothesis testing that defines the probability of rejecting a true null hypothesis, commonly denoted by alpha (α).

Test Statistic

A numerical value calculated from a sample used in statistical hypothesis testing to determine whether to reject the null hypothesis.

Normal Distribution

A probability distribution characterized by its symmetry surrounding the mean, demonstrating that data points close to the mean occur more frequently than those at a greater distance.

Degrees Of Freedom

Degrees Of Freedom represent the number of values in the final calculation of a statistic that are free to vary, often determining the shape of various sampling distributions.