The CONFIDENCE.T function in Google Sheets is a statistical tool designed to calculate the margin of error in estimating population means based on sample data when the population standard deviation is unknown. It aids researchers and analysts in understanding the reliability and precision of their sample estimates, allowing for informed decision-making in fields such as market research, healthcare, and social sciences.

Syntax

CONFIDENCE.T(alpha, standard_deviation, sample_size)

• alpha: Represents the significance level, which is the probability of rejecting the null hypothesis when it is true. A common value used is 0.05 for a 95% confidence level.
• standard_deviation: The estimated standard deviation of the population. This can be derived from the sample data or known from prior research.
• sample_size: The number of observations or samples being analyzed. It should be greater than one for the calculations to be valid.

Example #1

CONFIDENCE.T(0.05, 15, 30)

This function calculates the margin of error for a 95% confidence level, given a standard deviation of 15 and a sample size of 30, resulting in a value of approximately 4.10.

Example #2

CONFIDENCE.T(0.01, 10, 50)

Here, the function determines the margin of error for a 99% confidence level with a standard deviation of 10 and 50 samples, yielding a value of around 2.90.

Example #3

CONFIDENCE.T(0.025, 20, 40)

This example computes the margin of error for a 95% confidence level with a standard deviation of 20 and a sample size of 40, resulting in a value of roughly 5.29.

Error handling

• NUM!: This error occurs if the alpha value is not between 0 and 1, or if the sample_size is less than 2.
• DIV/0!: This message indicates that the standard_deviation or sample_size has led to division by zero in the calculation, typically when sample_size is 0.

Conclusion

In conclusion, the CONFIDENCE.T function is a vital statistical tool for estimating the margin of error when working with Student’s t-distribution. It provides valuable insights for researchers and analysts aiming to quantify uncertainty in their estimates, facilitating better-informed conclusions and decisions.