In this article, we will be looking at the approach to perform a one-proportion Z-test in the Python programming language.
Z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large.
One-proportion Z-test formula:
Where:
- P: Observed sample proportion
- Po: Hypothesized Population Proportion
- n: Sample size
The one-proportional Z-test uses the following null hypotheses:
- H0: p = p0 (population proportion is equal to hypothesized proportion p0)
The alternative hypothesis can be either two-tailed, left-tailed, or right-tailed:
- H1 (two-tailed): p ≠ p0 (two-tailed population proportion is not equal to some hypothesized value p0)
- H1 (left-tailed): p < p0 (left-tailed population proportion is less than some hypothesized value p0)
- H1 (right-tailed): p > p0 (right-tailed population proportion is greater than some hypothesized value p0)
Method 1: Calculating one-proportional Z-test using formula
In this approach, we will be calculating the one-proportional Z-test using the given formula and by simply putting the given value in the formula and getting the result.
Formula:
z=(P-Po)/sqrt(Po(1-Po)/n
In this example, we are using the P-value to 0.86, Po to 0.80, and n to 100, and by using this we will be calculating the z-test one proportional in the python programming language.
Python
import math P = 0.86Po = 0.80n = 100a = (P-Po) b = Po*(1-Po)/n z = a/math.sqrt(b) print(z) |
Output:
1.4999999999999984
Method 2: Calculating one-proportional Z-test using proportions_ztest() function
In this approach, we need to first import the statsmodels.stats.proportion library to the python compiler and then call the proportions_ztest() function to simpling get the one proportional Z-test by adding the parameters to the function.
proportions_ztest() function: This function is used to test for proportions based on the normal (z) test.
Syntax: proportions_ztest(count, nobs, value=None, alternative=’two-sided’)
Parameters:
- count: the number of successes in nobs trials.
- nobs: the number of trials or observations, with the same length as count.
- value: the hypothesized population proportion.
- alternative: The alternative hypothesis.
In this example, we will be using the same values as used in the previous example, and bypassing these values to the proportions_ztest() function we will be calculating the one-proportional z-test in the python programming language.
Python
# import library from statsmodels.stats.proportion import proportions_ztest # perform one proportion z-test proportions_ztest(count=80, nobs=100, value=0.86) |
Output:
(-1.4999999999999984, 0.1336144025377165)
