In this article, we will learn How to use the CONFIDENCE.NORM function in Excel.
What is confidence level and confidence interval?
In Statistics, when working with a normal distribution dataset. We find the sample mean of the sample dataset. For example finding the probability of winning the upcoming election by republicans or democrats. Or finding the amount of lead containing maggi packets is higher than the given limit. For these problems where the population dataset is infinite we calculate the values for the sample of data and predict the analysis for the population dataset. This interval around mean is also called the margin of error. Let's take an example where sample data (n) and calculate its mean (X) and standard deviation ( S ). Now to predict the estimation for the mean for the larger dataset, we use an interval called confidence interval around given confidence level. So the resulting confidence interval comes to be.
Here Z is a numerical value calculated based on the alpha (alpha = 1- confidence level). For 95% of confidence level, alpha comes out to be 0.05 and Z= 1.96. Mathematically we use the Z table to calculate the Z value. To calculate the confidence interval we need to calculate the margin of error and subtracting error value from mean value will give the lower limit of interval and adding the error value to mean value will give the upper limit of the interval. Let's calculate the margin of error in Excel using the CONFIDENCE.NORM function.
CONFIDENCE.NORM Function in Excel
CONFIDENCE.NORM takes the 3 numerical argument value of alpha, standard deviation and size of the sample dataset. The function returns the margin of error for the given alpha value. Let's understand these arguments stated below
CONFIDENCE.NORM Function syntax:
|=CONFIDENCE.NORM( alpha, standard_dev, size)|
alpha : value calculated using confidence level. 1 - confidence level
standard_dev : standard deviation for the given dataset.
size : sample size for the dataset.
All of these might be confusing to understand. Let's understand how to use the function using an example. Here we are given mean, standard deviation and size of the dataset.
Now we calculator the margin of error for the confidence level 90%. Alpha would be calculated using the formula (1-confidence level). Use this alpha argument in the formula stated below
Use the formula for 90% confidence level:
|=CONFIDENCE.NORM ( E2, B3, B4)|
The function returns the value 0.6579 which will be the margin of error for the 90% confidence level. Now calculate the margin of error for the 95% & 99% confidence level.
Use the formula for 95% confidence level:
|=CONFIDENCE.NORM ( E3, B3, B4)|
Similarly for the confidence level 99%. Use the alpha argument not the confidence level argument in the formula.
Use the formula for 99% confidence level:
|=CONFIDENCE.NORM ( E3, B3, B4)|
As you can see, increasing the confidence level, alpha decreases but the margin of error increases. Now calculate the confidence interval around the mean for the dataset.
Use the formula for lower limit of interval :
|= 36 - H2|
Use the formula for upper limit of interval :
|= 36 + H2|
Confidence interval for the 90%confidence level comes out to be [35.3421, 36.6579]. This gives a good idea for the overall population dataset. Similarly find out the confidence interval for different confidence level stated.
As you can see all the intervals are around the sample mean.
Here are all the observational notes using the CONFIDENCE.NORM function in Excel
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