The onesample proportion Ztest is a statistical tool used to conduct a hypothesis test about population proportions(p). It is used to estimate the difference between the proportion of responses(or number of successes) in sample data and the actual proportion in the population data from which we draw the sample.
What are the conditions required for conducting a onesample proportion z test?
Assumptions for the one sample proportion ztest are as follows:

The sample should be drawn at random from the population.

Population should follow a binomial distribution.

np0>10 & n(1p0)>10 where n is the sample size and p is the hypothesized value for the population proportion.

The population size should be 10 times larger than the sample size.
Hypothesis for the one sample proportion ztest
Let p0 denote the hypothesized value for the proportion.
p denotes the population proportion
Null Hypothesis:
H0: p=p0 The population proportion is equal to the hypothesized proportion.
Alternative Hypothesis: Three forms of alternative hypothesis are as follows:
Ha : p < p0 Population proportion is less than the hypothesized proportion. It is called the lowertail test (lefttailed test). Ha : p > p0 Population proportion is greater than the hypothesized proportion. It is called the Uppertail test(righttailed test). Ha : p ≠ p0 Population proportion is not equal to the hypothesized proportion. It is called a twotail test.
Calculating the Test Statistic
The test statistic for a onesample proportion Ztest is computed using the formula:
z = (p^  p0)/√(p0(1 p0 )/n where :

n: sample size

p^: observed sample proportion

p0: hypothesized population proportion
How do you find the zscore of a proportion?
We will calculate the zscore of a proportion by using one sample proportion ztest.
Procedure to find zscore using One Sample Proportion ZTest:

Define the Null Hypothesis and Alternate Hypothesis.

Decide the level of significance α (alpha).

Check the assumptions for the onesample proportion hypothesis ztest.

i.e. np0>10 & n(1p0)>10 where n is the sample size and p is the hypothesized value for the population proportion.

Calculate the test statistic using the formula mentioned above.

Find the critical value at a given significance level.

Determine the rejection criteria for the given confidence level.

Conclude the results whether the test statistic lies in the rejection region or nonrejection region.
Example of One Sample Z Proportion Test
In a sample of 1,000 people in Delhi,530 are tea drinkers and the rest are coffee drinkers. Can we assume that both tea and coffee drinkers are equally popular in the state at the 5% level of significance?
Solution:
Given data :

sample size (n) = 1000

Number of teadrinkers = 530

sample proportion = number of tea drinkers/sample size
p^ = 530/1000 = 0.53
Let’s solve this example with a stepbystep procedure.
Define the Null Hypothesis and Alternate Hypothesis:
let p be the population proportion for the tea drinkers.
Null Hypothesis: Both tea and coffee drinkers are equally popular in the state
H0 : p = 0.5
Alternate Hypothesis: Tea and Coffee drinkers are not equal in the state.
Ha : p ≠ 0.5
Level of significance (α): 0.05
Check Assumption:
Lets check the condition np0>10 & n(1p0)>10
here n=1000 & p0 = 0.5
np0 = 1000*0.5 = 500>10
n(1p0) = 1000(10.5) = 500 >10
Hence, both the conditions are satisfied so Here, we are able to use the one sample proportion test.
Calculate the test statistic (Z)
Use formula z = (p^ – p0)/√(p0(1 p0 )/n
z = (0.530.5)/ √ (0.5(10.5))/1000
z = 0.03/ √ (0.5*0.5)/1000
z = 1.89737
Find the critical value at a given significance level:
Use the Z Critical Value table for Various Confidence Levels
Critical Value at α =0.05 for twotailed test is zα = 1.960
Determine the rejection criteria for the given confidence level.
Decision Rule : If z ≤ zα or z ≥ zα then Reject H0
Conclusion:
Here z statistic = 1.89737 & zα = 1.96
Since zstatistic < zα i.e. 1.89737<1.96
There is not enough evidence to reject the null hypothesis. Hence it is not statistically significant.
Therefore, we accept the null hypothesis that both tea and coffee drinkers are equally popular in the state.
Conclusion
The onesample proportion ztest is used when you have categorical data, specifically a binary outcome (success /failure), and tests for differences in proportions.