By A. A. Walters (auth.)
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Similarly two standard deviations in excess of tho mean gives a value Xu which cuts off an upper tail of 2! per cent. Thus if the standard deviation of the normal sampling distribution is 36 METHODOLOGY, PROBABILITY AND SAMPLING known we can find any limits such as Xu, XL, etc. The standard deviation of the sampling distribution of the average is usually called the standard error of the mean. And the value of the standard error is derived from the standard deviation of the population. If standard deviation of family income in the population= a and number offamilies in the sample =n, then standard error of the average income of sample =a/Jn.
One might reasonably ask - suppose one has neither hunch, suspicions or prejudice, how then can one proceed to attach a value to P(A)? Of course, the simplest answer is to decide that Bayesian methods are not applicable. Without some prior probabilities we cannot construct a Bayesian solution. An alternative course is to invoke the 'principle of insufficient reason'. This simply means that we attribute to each of the alternative hypotheses an equal prior probability. Thus in our simple case the coin can either be unbiased or biased, thus the P(A) = l and the P(not A) = l· The main weaknesses of this 'principle' can easily be listed: there is no 'natural' classification of hypotheses.
Were 6o METHODOLOGY, PROBABILITY AND SAMPLING On the other hand an a priori probability may be based on nothing more substantial than a simple hunch, a vague suspicion or an irrational prejudice. One might reasonably ask - suppose one has neither hunch, suspicions or prejudice, how then can one proceed to attach a value to P(A)? Of course, the simplest answer is to decide that Bayesian methods are not applicable. Without some prior probabilities we cannot construct a Bayesian solution. An alternative course is to invoke the 'principle of insufficient reason'.