By IA. I Khurgin

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**Example text**

We will now approach the situation from the side of tlie supplier for whom a rejection of a good batch is the most unfavourable event, and so the rejection of a good batch will here be 40 Yes, No or May be assumed to be the first-type error. Let the probability of first-type error be a , then in a given set of tests the percentage of rejected true hypotheses will be 100a. 02 = == 2, and true hypothesis rejection will average 2 per cent. A measure of confidence that Hn is true (the batch is good) is here the probability 1 — a , called the confidence level.

Find out if the mean height changes from generation to generation assuming the normal height distribution. On the fairly reliable statistical evidence concerning the age groups born in the years 19081913, we can find the mean height of adult men in the age from 20 to 30, it is 162 centimetres. For the years 1943-1948 we obtain 170 centimetres. e. just a natural spread, since 41 Likelihood Ratio the mean height is a random variable. Our null hypothesis will be that the mean height in the 1943-1948 age group is the same as in the 19081913 age group, the alternative hypothesis being that the mean height has increased over these 35 years.

The main pur'pose of the traffic rules is to reduce the error probability. Here it is the firsttype error with the generally accepted null hypothesis: in crossing a street no accident will occur with me. At the same time thp false alarm, or second-type error, is here quite admissible, since it only implies t h a t you m a y wait a bit being overcautious. In our everyday life we cross streets, although we know t h a t an accident is possible, because we are guided by the practical confidence principle: if the probability of an event is small, it should Compromise 55 be thought t h a t in a single trial the event will not occur.

### Yes, no, or maybe (Science for every one) by IA. I Khurgin

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