Compatibility - CONFIDENCE Function

Description

The CONFIDENCE function returns the confidence interval for a population mean, using a normal distribution.

The confidence interval is a range of values. Your sample mean, x, is at the center of this range and the range is x ± CONFIDENCE. For any population mean μ₀, in this range, the probability of obtaining a sample mean further from μ₀ than x is greater than alpha.

For any population mean, μ₀, not in this range, the probability of obtaining a sample mean further from μ₀ than x is less than alpha.

In other words, assume that we use x, standard_dev, and size to construct a two-tailed test at significance level alpha of the hypothesis that the population mean is μ₀. Then we will not reject that hypothesis if μ₀ is in the confidence interval and will reject that hypothesis if μ₀ is not in the confidence interval.

The confidence interval does not allow us to infer that there is probability 1 – alpha that our next package will take a delivery time that is in the confidence interval.

Syntax

CONFIDENCE (alpha,standard_dev,size)

Arguments

Notes

• If we assume Alpha equals 0.05, we need to calculate the area under the standard normal curve that equals (1 - alpha), or 95 percent. This value is ± 1.96. The confidence interval is therefore −

  $$\bar{x}\pm1.96\left ( \frac{\alpha }{\sqrt{n}} \right )$$

• If Size is not an integer, it is truncated.

• If any argument is non-numeric, CONFIDENCE returns the #VALUE! error value.

• If Alpha is ≤ 0 or ≥ 1, CONFIDENCE returns the #NUM! error value.

• If Standard_dev ≤ 0, CONFIDENCE returns the #NUM! error value.

• If Size < 1, CONFIDENCE returns the #NUM! error value.

Example