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By A. A. Walters (auth.)

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P(G/1). We do not use the Bayesian concept of P(I/G); see below. ~ Thus we often read that a result is 'very significant'. 'only just', and so on. 58 METHODOLOGY, PROBABILITY AND SAMPLING but imagine that there is an enormous number of admissible hypotheses of average income, instead of merely two as we have in the Figure. Y average income of the population is possible. Now let us select a particular sample, and ask what is out~best estimator of the population average. It is intuitively clear that we should choose that value that gives the highest likelihood among competing hypotheses.

We take a random sample of roo families and measure their income. lf the hypothesis is true the average income of this sample should be a random drawing from the sampling distribution of the sample averages. a. e. one chance in 40. By most people's ideas one chance in forty denotes an unlikely event. a. we should say that the hypothesis is discredited. We should 'reject' the hypothesis. In one out offorty cases we should, of course, be wrong in making statements of this kind- since there is a 0·025 chance that values as low as this, or lower, will occur when the population average is £r,ooo.

If the government allocates contracts to three firms at random with a constant probability of l for each firm, and ifeach firm has a o·g chance of making a profit if it gets a contract, find the probability that a particular firm will make a profit if there are 9 contracts awarded. 3 Statistical Inference Significance The main applications of probability concepts are in sampling. The problem is to distil as much information as we can from a sample of the observations of the process in which we are interested.

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