Statistics: binotest

### Function Reference: `binotest`

statistics: [h, pval, ci] = binotest (pos, N, p0)
statistics: [h, pval, ci] = binotest (pos, N, p0, Name, Value)

Test for probability p of a binomial sample

Perform a test of the null hypothesis p == p0 for a sample of size N with pos positive results.

Name-Value pair arguments can be used to set various options. `"alpha"` can be used to specify the significance level of the test (the default value is 0.05). The option `"tail"`, can be used to select the desired alternative hypotheses. If the value is `"both"` (default) the null is tested against the two-sided alternative `p != p0`. The value of pval is determined by adding the probabilities of all event less or equally likely than the observed number pos of positive events. If the value of `"tail"` is `"right"` the one-sided alternative `p > p0` is considered. Similarly for `"left"`, the one-sided alternative `p < p0` is considered.

If h is 0 the null hypothesis is accepted, if it is 1 the null hypothesis is rejected. The p-value of the test is returned in pval. A 100(1-alpha)% confidence interval is returned in ci.

Source Code: binotest

### Example: 1

     % flip a coin 1000 times, showing 475 heads
     % Hypothesis: coin is fair, i.e. p=1/2
     [h,p_val,ci] = binotest(475,1000,0.5)
     % Result: h = 0 : null hypothesis not rejected, coin could be fair
     %         P value 0.12, i.e. hypothesis not rejected for alpha up to 12%
     %         0.444 <= p <= 0.506 with 95% confidence

    h = 0
    p_val = 0.1212
    ci =

       0.4437   0.5065

### Example: 2

     % flip a coin 100 times, showing 65 heads
     % Hypothesis: coin shows less than 50% heads, i.e. p<=1/2
     [h,p_val,ci] = binotest(65,100,0.5,'tail','left','alpha',0.01)
     % Result: h = 1 : null hypothesis is rejected, i.e. coin shows more heads than tails
     %         P value 0.0018, i.e. hypothesis not rejected for alpha up to 0.18%
     %         0 <= p <= 0.76 with 99% confidence

    h = 1
    p_val = 1.7588e-03
    ci =

            0   0.7580