The one proportion test is a statistical test used in Six Sigma and other process improvement methodologies to determine whether a process is statistically different from a target value. This test can be used when the data are binary (e.g., pass/fail), or when the data can be converted to binary form (e.g., defects per unit). The one proportion test is also known as the null hypothesis significance test (NHST).

## 1 Proportion Test

The purpose of the one proportion test is to compare the proportions of two groups. The null hypothesis states that there is no difference between the two groups, while the alternative hypothesis states that there is a difference.

To conduct a one-proportion test, we first need to calculate the pooled proportion, which is the weighted average of the two group proportions. We then calculate the standard error of the proportion, which is used to calculate the z-score. The z-score tells us how many standard deviations away from the mean our observed proportion is.

If our z-score is less than -1.96 or greater than 1.96, we can reject the null hypothesis and conclude that there is a statistically significant difference between the two groups. If our z-score is between -1.96 and 1.96, we cannot reject the null hypothesis and must conclude that there is not a statistically significant difference between the two groups.

## Conclusion:

In conclusion, the one proportion test is a statistical test used in Six Sigma and other process improvement methodologies to determine whether a process is statistically different from a target value. This test can be used when the data are binary (e.g., pass/fail), or when the data can be converted to binary form (e.g., defects per unit). The one proportion test is also known as the null hypothesis significance test (NHST).