CONFIDENCE_T

Updated 2023-11-02 21:25:25.513000

Syntax

SELECT [westclintech].[wct].[CONFIDENCE_T](
  <@Alpha, float,>
 ,<@Standard_dev, float,>
 ,<@Size, float,>)

Description

Use the scalar function CONFIDENCE_T to calculate a confidence interval when you don't know the population standard deviation and are using the sample standard deviation instead.

Arguments

@Alpha

The significance level used to calculate the confidence interval. @Alpha must be of a type float or of type that intrinsically converts to float.

@Size

The sample size. @Size must be of a type float or of a type the intrinsically converts to float.

@Standard_dev

The sample standard deviation. @Standard_dev must be of a type float or of a type that intrinsically converts to float.

Return Type

float

Remarks

0 < @Alpha < 1.

0 < Standard_dev.

0 < @Size.

Examples

Given a sample standard deviation of 14.67, calculate the 95% confidence interval for a sample size of 50.

SELECT wct.CONFIDENCE_T(   .05,   --@Alpha

                           14.67, --@Standard_dev

                           50     --@Size

                       ) as CI;

This produces the following result.

{"columns":[{"field":"CI","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"CI":"4.16916787012236"}]}

The CONFIDENCE_T function is closely related to the T_INV function.

SELECT wct.CONFIDENCE_T(alpha, mu, sigma) as CI,

       wct.T_INV(1 - alpha * 0.5, sigma - 1) * mu / SQRT(sigma) as CI

FROM

(

    VALUES

        (0.05, 14.67, 50)

) n (alpha, mu, sigma);