What excel command do we use to get the confidence interval margin of error for the t-distribution?

In this article, we will learn How to use the CONFIDENCE.T function in Excel.

What is confidence level and confidence interval?

In Statistics, when working with a student's t-distribution dataset, where we need to analyse the population mean and standard deviation given information about the sample dataset. confidence interval for a population mean, using a Student's t distribution. For example finding the probability of winning an election by ruling or opposition party by taking the sample poll votes. Or finding the amount of lead containing maggi packets is higher than the given limit, given the sample mean and standard deviation. For these problems where the population dataset is infinite and we calculate the values from the sample 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.T function.

CONFIDENCE.T Function in Excel

CONFIDENCE.T 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.T Function syntax:

=CONFIDENCE.T( 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.

Example :

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 sample student's t distribution dataset. Using this we need to find the confidence interval for the population 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.T ( E2, B3, B4)

The function returns the value 0.6642 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.T ( 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.T ( E3, B3, B4)

As you can see, increasing the confidence level, alpha decreases but the margin of error increases.

Confidence Interval

Now calculate the confidence interval around the mean from the sample dataset for the population dataset.

Use the formula for lower limit of interval :

and

Use the formula for upper limit of interval :

Confidence interval for the 90%confidence level comes out to be [35.3358, 36.6642]. This gives a good idea for the overall population dataset. Similarly find out the confidence interval for different confidence level stated below.

As you can see all the intervals are around the sample mean. This is based on a Student's t-distribution.

Here are all the observational notes using the CONFIDENCE.T function in Excel
Notes :

The function only works with numbers. If any argument other than cumulative is non-numeric, the function returns #VALUE! error.
The function returns #NUM! Error. If alpha < 0 and alpha > 1
Value in decimal or value in percentage is the same value in Excel. Convert the value to percentage, if required.
You can feed the arguments to the function directly or using the cell reference as explained in the example.

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