hypothesis. If it is small we reject our hypothesis and must accept our alternative 
hypothesis Hi : o > 5.0 ym. 
Our problem is to find the value, C, the critical value, of the computed standard 
error that divides our sample distribution into an acceptance region and a rejection 
region. 
This will be done on a certain level of significance, « 96, which is the maximum 
risk of rejecting Ho when Ho is true. The test will also be made with a certain 
power function. The power, I—5, of the test is the probability of rejecting Ho 
when Hi is true. The power is a function of the degrees of freedom, f, in the test, 
and the level of significance, y, and on the true value of the unknown o. (Higher 
power for greater f and for greater 6/00.) A subproblem is thus to determine 
two?) of the three parameters o, (9 and f. The classical statistical theory does not 
give us any help as to how to make this determination). Thus we have to introduce 
the decision theory below to obtain the optimum balance among the risks for 
different types of decision errors and the costs of these errors and also the cost of 
sampling and the marginal value of the sample. 
For a certain œ, B and f we can summarize our action-outcome-scheme thus: 
  
Decision The true (but unknown) state of nature 
— Action Ho: o 27 5.0 um He 50,m 
  
Accept Ho, i. e. accept 
; Correct decision. Wrong decision, Jf-error. 
the instrument ...... ; 8 | B 
  
Reject Ho, i. e. reject Wrong decision, a-error, Correct decision, made 
the instrument ...... . made with the maxi- with the probability 
mum probability of « 96. 1—], i. e. the power. 
  
Introduction of decision theory 
History 
Game theory was introduced by Emile Borel in 1921. Abraham Wald, 
called the father of present day decision theory, made his innovations 
at the beginning of World War II, his classical work, [7], being from 
1950. Since 1958, the volume of publications on decision making "has 
grown dramatically", see [9]. Most of the theory may be described as 
formalised common sense. 
Basic Terminology and Concepts 
A choice must be made from several possible acts. The chosen act will 
ultimately lead to some definite profit (possibly negative), but for at least 
4) This is when a specified probability distribution function is assumed. 
5) The resolution II: 6 at the Lisbon Congress to use «y — 5 % is of course 
not applicable in our case, which the resolution also says. It is e. g. in theoretical 
tests where no practical considerations, such as costs, are involved that the a = 
5 % is recommended. 
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