This One Proportion Z-Test Calculator helps you analyze a single sample proportion when testing against a hypothesized population proportion . For example, you could test if the success rate of a manufacturing process differs from a target value, or if a sample proportion represents a significant change from a known population proportion. The calculator performs comprehensive statistical analysis including hypothesis testing and generates publication-ready reports. Enter your number of successes and total trials below to begin the analysis. for a quick example.
One-Proportion Z-Test is used to test if a population proportion is significantly different from a hypothesized value. It's commonly used for analyzing success rates, percentages, or proportions in a single group.
Test Statistic:
Where:
Confidence Interval:
Where and are the critical values for the desired confidence level.
Testing if a new manufacturing process meets quality standards:
Z-statistic:
For two-tailed test:
Critical value at 5% significance level:
Since and , we fail to reject . There is insufficient evidence to conclude that the process quality differs from the standard level.
Cohen's h for one proportion:
Interpretation:
Required sample size for desired power:
Where:
x <- 45 # Number of successes
n <- 100 # Number of trials
p <- 0.5 # Null hypothesis proportion
# Perform one-proportion test
result <- prop.test(
x = x,
n = n,
p = p,
alternative = "two.sided",
correct = FALSE # No continuity correction
)
# Print results
print(result)from statsmodels.stats.proportion import proportions_ztest
import numpy as np
from scipy import stats
# Example data
p0 = 0.5
success1, n1 = 45, 100
p1 = success1 / n1
# Perform one-proportion z-test
zstat, pvalue = proportions_ztest(
success1, n1, value=p0, alternative='two-sided'
)
print(f'z-statistic: {zstat:.4f}')
print(f'p-value: {pvalue:.4f}')
# construct confidence interval
alpha = 0.05
z_critical = stats.norm.ppf(1 - alpha / 2)
margin_of_error = z_critical * np.sqrt((p1 * (1 - p1) / n1))
prop_diff = p1
ci_lower = prop_diff - margin_of_error
ci_upper = prop_diff + margin_of_error
print(f'Confidence interval: ({ci_lower:.4f}, {ci_upper:.4f})')Consider these alternatives when assumptions are violated:
This One Proportion Z-Test Calculator helps you analyze a single sample proportion when testing against a hypothesized population proportion . For example, you could test if the success rate of a manufacturing process differs from a target value, or if a sample proportion represents a significant change from a known population proportion. The calculator performs comprehensive statistical analysis including hypothesis testing and generates publication-ready reports. Enter your number of successes and total trials below to begin the analysis. for a quick example.
One-Proportion Z-Test is used to test if a population proportion is significantly different from a hypothesized value. It's commonly used for analyzing success rates, percentages, or proportions in a single group.
Test Statistic:
Where:
Confidence Interval:
Where and are the critical values for the desired confidence level.
Testing if a new manufacturing process meets quality standards:
Z-statistic:
For two-tailed test:
Critical value at 5% significance level:
Since and , we fail to reject . There is insufficient evidence to conclude that the process quality differs from the standard level.
Cohen's h for one proportion:
Interpretation:
Required sample size for desired power:
Where:
x <- 45 # Number of successes
n <- 100 # Number of trials
p <- 0.5 # Null hypothesis proportion
# Perform one-proportion test
result <- prop.test(
x = x,
n = n,
p = p,
alternative = "two.sided",
correct = FALSE # No continuity correction
)
# Print results
print(result)from statsmodels.stats.proportion import proportions_ztest
import numpy as np
from scipy import stats
# Example data
p0 = 0.5
success1, n1 = 45, 100
p1 = success1 / n1
# Perform one-proportion z-test
zstat, pvalue = proportions_ztest(
success1, n1, value=p0, alternative='two-sided'
)
print(f'z-statistic: {zstat:.4f}')
print(f'p-value: {pvalue:.4f}')
# construct confidence interval
alpha = 0.05
z_critical = stats.norm.ppf(1 - alpha / 2)
margin_of_error = z_critical * np.sqrt((p1 * (1 - p1) / n1))
prop_diff = p1
ci_lower = prop_diff - margin_of_error
ci_upper = prop_diff + margin_of_error
print(f'Confidence interval: ({ci_lower:.4f}, {ci_upper:.4f})')Consider these alternatives when assumptions are violated: