CONFIDENCE.NORM

Calculates the confidence interval for a population mean based on the normal distribution.

Syntax:

CONFIDENCE.NORM(alpha, standard_dev, size)

alpha is required, and is the significance level.

standard_dev is required, and is the known standard deviation of the population.

size is required, and is the sample size.

Example:

If alpha contains 0.05, standard_dev contains 10 and size contains 100:

CONFIDENCE.NORM(0.05, 10, 100)

returns 1.959963985

Alpha:

Standard_dev:

Size:

Result:

1.959963985

Application:

Imagine you are a quality control manager at a factory that produces light bulbs. You want to estimate the average lifespan of all light bulbs produced by the factory, but you cannot test every single one. Instead, you take a random sample of light bulbs and test their lifespan.

Here is the data you have:

Sample Mean ( $\overset{x}{ˉ}$ ): The average lifespan of your sample of light bulbs is 1,200 hours.
Population Standard Deviation (σ): Based on historical data and the manufacturing process, the population standard deviation for the lifespan of these light bulbs is known to be 150 hours.
Sample Size (n): You randomly selected and tested 100 light bulbs.
Confidence Level: You want to be 95% confident in your estimate. This means the significance level (α) is 1 - 0.95 = 0.05.

The CONFIDENCE.NORM function calculates the margin of error, which is the value you add to and subtract from the sample mean to create the confidence interval.

Formula:

The mathematical formula behind the CONFIDENCE.NORM function is:

$Margin of Error = z_{α /2} \times \frac{σ}{n}$

Where:

zα/2 is the z-score associated with the desired confidence level. For a 95% confidence level (α=0.05), the z-score is approximately 1.96.
σ is the known population standard deviation.
n is the sample size.

Calculating the Confidence Interval:

The syntax would be:

CONFIDENCE.NORM(alpha, standard_dev, size)

In our example, the formula would be:

CONFIDENCE.NORM(0.05, 150, 100)

Table of Values:

	Parameter	Value
	A	B
1	Significance Level (α)	0.05
2	Population Standard Deviation (σ)	150
3	Sample Size (n)	100
4	Result of CONFIDENCE.NORM	29.4

Interpretation:

The CONFIDENCE.NORM function returns a margin of error of 29.4 hours.

To find the confidence interval, you take your sample mean and add and subtract the margin of error:

Lower Bound: Sample Mean - Margin of Error = 1,200 - 29.4 = 1,170.60 hours
Upper Bound: Sample Mean + Margin of Error = 1,200 + 29.4 = 1,229.40 hours

Conclusion:

Based on your sample of 100 light bulbs, you can state with 95% confidence that the true average lifespan of all light bulbs produced by the factory is between 1,170.6 hours and 1,229.4 hours. This provides a more precise and statistically sound estimate than simply stating the sample mean of 1,200 hours.

Result for Lower Bound:

1170.6

Result for Upper Bound:

1229.4