The Dollar Department Store Chain Has the Opportunity of Acquiring $\quad\quad\quad\quad\quad\quad\text{State Of The Economy}\\\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Over The Next 5 Years}$

question 26

Short Answer

The Dollar Department Store chain has the opportunity of acquiring either 3,5,or 10 leases from the bankrupt Granite Variety Store chain.Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years.There are four possible states of the economy as modeled by Dollar Department Stores and its president estimates P(s₁)= .4,P(s₂)= .3,P(s₃)= .1,and P(s₄)= .2.The utility has also been estimated.Given the payoffs (in $1,000,000's)and utility values below,which decision should Dollar make? Payo ff Table $\quad\quad\quad\quad\quad\quad\text{State Of The Economy}\\\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Over The Next 5 Years}$
$\begin{array}{l|rrrr}Decision&s_{1} &s_{2} &s_{3} &s_{4} \\\hlined_{1}--\text { buy } 10 \text { leases } & 10 & 5 & 0 & -20 \\d_{2}--\text { buy } 5 \text { leases } & 5 & 0 & -1 & -10 \\d_{3}--\text { buy 3 leases } & 2 & 1 & 0 & -1 \\d_{4}--\text { do not buy } & 0 & 0 & 0 & 0\end{array}$ Utility Table $$\begin{array} { l r r r r r r r } \text { Payoff } ( \text { in } \$ 1,000,000 ' s ) & + 10 & + 5 & + 2 & 0 & - 1 & - 10 & - 20 \\\hline \text { Utility } & + 10 & + 5 & + 2 & 0 & - 1 & - 20 & - 50\end{array}$$

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Definitions:

Statistically Significant

A determination that a relationship observed in a dataset is unlikely to have occurred by chance, according to a predefined significance level.

Significance Level

This is the probability of rejecting the null hypothesis when it is true, usually denoted by alpha (α), and used as a threshold for determining statistical significance.

Null Hypothesis

A hypothesis that states there is no significant difference or effect, typically to be tested against an alternative hypothesis.

Expected Number

A statistical term referring to the calculated average or mean value anticipated in a probability distribution or experiment.