## One Proportion Z-Test

Do you ever wonder if your hypothesis about a certain proportion is valid? One way to answer that question is through a

One Proportion Z-Test.

## Null and Alternative Hypotheses

Before we dive into the test itself, let us first discuss the

Null and Alternative Hypotheses. The Null Hypothesis is the statement that assumes there is no significant difference or relationship between the variables being tested.

On the other hand, the Alternative Hypothesis states that a significant difference exists. In a

One Proportion Z-Test, the Null Hypothesis assumes that the proportion is equal to a given value, while the Alternative Hypothesis assumes that the proportion is different from the given value.

## Test Statistic Formula

## The next step is to compute for the Test Statistic using the formula:

z = (p – P) / sqrt(P*(1-P)/n)

## where

– p is the observed sample proportion

– P is the hypothesized population proportion

– n is the sample size

The value of z will be computed based on the difference between the observed and hypothesized proportions, as well as the sample size.

## Interpretation of Results

After computing for the Test Statistic, the next step is to interpret the results. The p-value is obtained from the Z-Table, which can be compared to a predetermined Significance Level.

If the p-value is less than the Significance Level, then we reject the Null Hypothesis in favor of the Alternative Hypothesis. On the other hand, if the p-value is greater than the Significance Level, then we fail to reject the Null Hypothesis.

## Python Implementation

## Now that we understand the theory behind the

One Proportion Z-Test, let us see how it can be implemented in Python using the proportions_ztest() function.

## Function Syntax

The basic syntax of the proportions_ztest() function is:

proportions_ztest(count, nobs, value=None, alternative=’two-sided’, prop_var=False)

## where

– count is the number of successes in the sample

– nobs is the sample size

– value is the hypothesized proportion (default value is 0.5)

– alternative is the type of Alternative Hypothesis (default is ‘two-sided’)

– prop_var is a boolean value that determines the use of the sample proportion or hypothesized proportion (default is False)

## Example Scenario

Suppose we want to test the hypothesis that the proportion of residents in a certain city who support a particular law is equal to 0.6. We surveyed 500 residents and found that 320 of them support the law. To test this hypothesis using the proportions_ztest() function, we can input the following values:

– count = 320

– nobs = 500

– value = 0.6

## Output Interpretation

The output of the proportions_ztest() function will provide us with the Z-Score and the p-value. If we set the Significance Level to 0.05, then we can interpret the output as follows:

– Z-Score: 1.6974

– p-value: 0.0894

Since the p-value is greater than the Significance Level, we fail to reject the Null Hypothesis.

We can therefore conclude that there is not enough evidence to support the claim that the proportion of residents who support the law is different from 0.6.

In conclusion, the

One Proportion Z-Test is a useful statistical tool in hypothesis testing. By formulating

Null and Alternative Hypotheses, computing for the Test Statistic, and interpreting the results based on a predetermined Significance Level, we can determine whether or not our hypothesis is valid.

With the help of the proportions_ztest() function in Python, implementing the

One Proportion Z-Test is made easier and more efficient. In summary, the

One Proportion Z-Test is a statistical method used to test the null and alternative hypotheses for proportion-related tests.

## The test statistic formula and interpretation of the results are crucial in understanding the

One Proportion Z-Test. Additionally, the proportions_ztest() function in Python simplifies the process by providing a quick output of the Z-Score and p-value.

## It is essential to correctly formulate the

Null and Alternative Hypotheses and determine the Significance Level before interpreting the results. By knowing the basics of the

One Proportion Z-Test and being able to implement it in Python, one gains a better understanding of how to perform hypothesis testing accurately.