# CONFIDENCE.T

The `CONFIDENCE.T` function calculates the confidence interval for a one-tailed Student's t-distribution. This function is commonly used in statistics to determine the range of values likely to contain an unknown population parameter with a certain level of confidence. The result of the function is the range of values around the sample mean, where the population mean is expected to fall within a certain confidence level.

## Usage

Use the `CONFIDENCE.T` formula with the syntax shown below, it has 3 required parameters:

Parameters:
1. alpha (required):
The significance level used to compute the confidence level. Must be between 0 and 1.
2. standard_deviation (required):
The standard deviation of the population.
3. size (required):
The sample size.

## Examples

Here are a few example use cases that explain how to use the `CONFIDENCE.T` formula in Google Sheets.

### Calculating the confidence interval for a sample mean

Suppose you have a sample of size 30, with a mean of 100 and a standard deviation of 10. You want to calculate the 95% confidence interval for the population mean. You can use the `CONFIDENCE.T` function with `alpha=0.05`, `standard_deviation=10`, and `size=30`.

### Testing the difference between two means

Suppose you have two samples, with means of 100 and 110, and standard deviations of 10 and 12, respectively. You want to test if the difference between the two means is statistically significant at a 90% confidence level. You can use the `CONFIDENCE.T` function to calculate the confidence interval for the difference in means, and check if it includes 0.

### Estimating the sample size

Suppose you want to estimate the sample size required to estimate the population mean with a margin of error of 5, and a 95% confidence level. You can use the `CONFIDENCE.T` function to solve for `size`.

## Common Mistakes

`CONFIDENCE.T` not working? Here are some common mistakes people make when using the `CONFIDENCE.T` Google Sheets Formula:

### Incorrect order of arguments

Make sure to enter the arguments in the correct order: alpha, standard deviation, size.

### Invalid alpha value

The alpha value must be between 0 and 1. Check that the value entered is within this range.

### Invalid standard deviation

Make sure that the standard deviation value is positive and that it is the correct value for the population or sample being analyzed.

### Invalid sample size

Make sure that the sample size entered is a positive integer and large enough for the confidence interval desired.

The following functions are similar to `CONFIDENCE.T` or are often used with it in a formula:

• `T.DIST`

The `T.DIST` function returns the probability of a Student's t-distribution with a specified degrees of freedom. This function is usually used in hypothesis testing to determine the probability that a sample mean is within a specified range of values.

• `T.DIST.2T`

The `T.DIST.2T` function returns the two-tailed probability of the Student's t-distribution. This function is commonly used in hypothesis testing to determine if two sets of data have different means. It is also used in confidence interval estimation, where it calculates the probability that the difference between two population means falls within a specified range.

• `T.INV`

The `T.INV` function returns the inverse of the Student's t-distribution for the provided probability and degrees of freedom. This function is commonly used to calculate a critical value from the t-distribution when working with small sample sizes.

• `T.INV.2T`

The `T.INV.2T` function returns the two-tailed inverse of the t-distribution. This is commonly used in hypothesis testing to determine the critical value of t for a given level of significance and degrees of freedom.

You can learn more about the `CONFIDENCE.T` Google Sheets function on Google Support.