Fairco,a family business,is considering making an investment in its manufacturing operation.Three decisions are under consideration: (1) a large investment; (2) a medium investment;and (3) a small investment.The business believes that there are three possible future outcomes for its product: (1) increasing demand; (2) stable demand;and (3) decreasing demand.The business believes that the probability for increasing,stable and decreasing product demand are 0.4,0.5,and 0.1,respectively.The following payoff table describes the decision situation. 
The expected value for the small investment decision is
Definitions:
Alternative Hypotheses
In statistical hypothesis testing, it is the hypothesis that proposes a difference or effect, in contrast to the null hypothesis which proposes no effect or relationship.
Type II Error
Refers to the error that occurs when a statistical test fails to reject a false null hypothesis.
Type I Error
Falsely rejecting a true null hypothesis, widely recognized as a "false positive."
Control Limits
The bounds used in control charts to signal when a process is in or out of control, based upon the statistical properties of the monitored process.
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