By Collett, D
Advent a few Examples The Scope of this ebook Use of Statistical software program STATISTICAL INFERENCE FOR BINARY facts The Binomial Distribution Inference concerning the good fortune chance comparability of 2 Proportions comparability of 2 or extra Proportions types FOR BINARY AND BINOMIAL facts Statistical Modelling Linear versions tools of Estimation becoming Linear versions to Binomial facts versions for Binomial reaction Data Read more...
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In examples such as this, an hypothesis test is used to indicate whether or not the data are in accord with the pre-specified value of the success probability. Suppose that it is desired to test the hypothesis that the true success probability, p, takes the particular value p0 . This hypothesis, which is termed the null hypothesis, is the hypothesis that will be acted on unless the data indicate that it is untenable. The null hypothesis is denoted by H0 , and the hypothesis itself is written as H0 : p = p0 .
10) is large, that is if P(Z z) is sufficiently small. 30 STATISTICAL INFERENCE FOR BINARY DATA If the alternative to the null hypothesis is the two-sided alternative hypothesis H1 : p = p0 , large negative and large positive values of z will suggest that the null hypothesis is false. Consequently, we now require the probability that a standard normal random variable has a value as extreme or more extreme than |z| = √ |ˆ p − p0 | , {p0 (1 − p0 )/n} where the notation |z| denotes the modulus or absolute value of z, that is, the unsigned value of z.
N When y = 0, is the number of ways that n zeros can occur in n 0 observations. This is just one, since the sequence of observations is 0000 . . Now, n! 1 n = = , 0 0! × n! 0! and so for this to be equal to unity, 0! must be defined to be equal to one. This extends the definition of the factorial function to all non-negative integers. The total probability of obtaining a sequence of y ones and n − y zeros, n independent of the ordering of the binary observations, will be multiplied 0 by the probability of any particular arrangement of the y ones and n−y zeros.