1 Proportion Z Test Calculator

1 Proportion Z Test Formula:

\[ z = \frac{p - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \]

Sample Proportion (p):

proportion

Hypothesized Proportion (p₀):

proportion

Sample Size (n):

count

Z-Score (z):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the 1 Proportion Z Test?

The 1 Proportion Z Test is a statistical hypothesis test used to determine whether a sample proportion differs significantly from a hypothesized population proportion. It's commonly used in quality control, medical studies, and social sciences to test claims about population proportions.

2. How Does the Calculator Work?

The calculator uses the 1 Proportion Z Test formula:

\[ z = \frac{p - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \]

Where:

\( p \) — Sample proportion (observed proportion)
\( p_0 \) — Hypothesized population proportion
\( n \) — Sample size (number of observations)
\( z \) — Z-score (test statistic)

Explanation: The formula calculates how many standard errors the sample proportion is away from the hypothesized proportion. A larger absolute z-score indicates stronger evidence against the null hypothesis.

3. Importance of Z-Score Calculation

Details: The z-score is crucial for determining statistical significance in hypothesis testing. It helps researchers decide whether to reject or fail to reject the null hypothesis by comparing the calculated z-score to critical values from the standard normal distribution.

4. Using the Calculator

Tips: Enter the sample proportion (between 0 and 1), hypothesized proportion (between 0 and 1), and sample size (positive integer). All values must be valid and within appropriate ranges.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a 1 Proportion Z Test?
A: Use this test when you want to compare a sample proportion to a known or hypothesized population proportion, and when your sample size is sufficiently large (typically n > 30).

Q2: What does the z-score tell me?
A: The z-score indicates how many standard errors your sample proportion is from the hypothesized proportion. Higher absolute values suggest stronger evidence against the null hypothesis.

Q3: What are typical critical z-values?
A: For a two-tailed test at α = 0.05, critical values are ±1.96. For α = 0.01, they are ±2.58. For one-tailed tests, use ±1.645 (α = 0.05) or ±2.326 (α = 0.01).

Q4: Are there assumptions for this test?
A: Yes, the test assumes that the sample is random, observations are independent, and the sample size is large enough that both np₀ and n(1-p₀) are greater than 5.

Q5: How do I interpret the results?
A: Compare your calculated z-score to critical values. If |z| > critical value, reject the null hypothesis. You can also calculate the p-value from the z-score using standard normal distribution tables.