Tutoring statistics, the tutor is happy to share the CONFIDENCE.T() function from LibreOffice Calc.
While the CONFIDENCE() function assumes the population standard deviation is known, I pointed out that, with sample size n≥31, the t-distribution approximates the normal closely enough that the sample standard deviation can be used. Today, I’ll make a direct comparison.
Yesterday’s post considered a sample mean of 67.3, known population standard deviation of 12.4, and sample size 42. The input
gave the result 3.75, meaning a confidence interval of 67.3±3.75, or 63.55 to 71.05.
LibreOffice Calc’s CONFIDENCE.T() function has the following format:
=confidence(1-confidence_level, sample_standard_deviation, sample_size)
Since it uses the sample standard deviation, CONFIDENCE.T() calculates the confidence interval from the t-distribution. By constrast, CONFIDENCE() takes the population standard deviation, so uses the normal distribution to calculate the confidence interval.
The following input
=confidence.t(0.05, 12.4, 42)
gives the result 3.864, implying a confidence interval of 67.3±3.864 or 63.44 to 71.16. Obviously this is not much different from the confidence interval 63.55 to 71.05 gotten using =confidence(0.05,12.4,42).
So, the CONFIDENCE.T() function seems to demonstrate that, for a sample size n≥31, the t-distribution approximates the normal distribution closely enough that the sample standard deviation can be used when the population standard deviation is unavailable.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.