oneSampleProportionCI(k, n, CL)
Overview
The oneSampleProportionCI function calculates a confidence interval for a proportion in a statistical population, based on the proportion observed in a sample. The function employs the Wald-Agresti-Coull (WAC) method, a modified version of the standard Wald method to calculate the confidence interval.
Parameters
| Parameter | Type | Description | Default |
|---|---|---|---|
k |
Number | Number of successful outcomes in the sample. | - |
n |
Number | Total number of trials in the sample. | - |
CL |
Number | Confidence level for the confidence interval. | 0.95 |
Returns
| Return | Type | Description |
|---|---|---|
pHat |
Number | The estimated proportion based on the sample. |
lowerCI |
Number | Lower bound of the confidence interval for the proportion. |
upperCI |
Number | Upper bound of the confidence interval for the proportion. |
testType |
String | Specifies the type of test conducted, in this case, "One Sample Proportion CI". |
Example
local k = 55
local n = 100
local CL = 0.95
local result = oneSampleProportionCI(k, n, CL)
print(result.pHat, result.lowerCI, result.upperCI, result.testType) -- Output will vary based on the input
Mathematical Background
The estimated proportion \hat{p} is calculated as:
\hat{p} = \frac{k + 2}{n + 4}
The standard error SE of the estimated proportion is calculated using:
SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n + 4}}
The confidence interval is given by:
\text{Lower CI} = \hat{p} - Z_{\alpha/2} \times SE
\text{Upper CI} = \hat{p} + Z_{\alpha/2} \times SE
where Z_{\alpha/2} is the value from the inverse of the standard normal distribution corresponding to a 1- \alpha/2 confidence level.