# scipy.stats.binomtest#

scipy.stats.binomtest(k, n, p=0.5, alternative='two-sided')[source]#

Perform a test that the probability of success is p.

The binomial test  is a test of the null hypothesis that the probability of success in a Bernoulli experiment is p.

Details of the test can be found in many texts on statistics, such as section 24.5 of .

Parameters:
kint

The number of successes.

nint

The number of trials.

pfloat, optional

The hypothesized probability of success, i.e. the expected proportion of successes. The value must be in the interval `0 <= p <= 1`. The default value is `p = 0.5`.

alternative{‘two-sided’, ‘greater’, ‘less’}, optional

Indicates the alternative hypothesis. The default value is ‘two-sided’.

Returns:
result`BinomTestResult` instance

The return value is an object with the following attributes:

kint

The number of successes (copied from `binomtest` input).

nint

The number of trials (copied from `binomtest` input).

alternativestr

Indicates the alternative hypothesis specified in the input to `binomtest`. It will be one of `'two-sided'`, `'greater'`, or `'less'`.

statisticfloat

The estimate of the proportion of successes.

pvaluefloat

The p-value of the hypothesis test.

The object has the following methods:

proportion_ci(confidence_level=0.95, method=’exact’) :

Compute the confidence interval for `statistic`.

Notes

New in version 1.7.0.

References



Jerrold H. Zar, Biostatistical Analysis (fifth edition), Prentice Hall, Upper Saddle River, New Jersey USA (2010)

Examples

```>>> from scipy.stats import binomtest
```

A car manufacturer claims that no more than 10% of their cars are unsafe. 15 cars are inspected for safety, 3 were found to be unsafe. Test the manufacturer’s claim:

```>>> result = binomtest(3, n=15, p=0.1, alternative='greater')
>>> result.pvalue
0.18406106910639114
```

The null hypothesis cannot be rejected at the 5% level of significance because the returned p-value is greater than the critical value of 5%.

The test statistic is equal to the estimated proportion, which is simply `3/15`:

```>>> result.statistic
0.2
```

We can use the proportion_ci() method of the result to compute the confidence interval of the estimate:

```>>> result.proportion_ci(confidence_level=0.95)
ConfidenceInterval(low=0.05684686759024681, high=1.0)
```