Tutoring statistics, you realize how convenient using a spreadsheet can be.
In yesterday’s post I mentioned some theoretical points about two-sided confidence intervals for the population mean.
On the practical side, if you simply need a confidence interval for the population mean, you can use Excel’s CONFIDENCE() function, which works the same on LibreOffice Calc. It has the following format:
=confidence(1-confidence_level, pop_standard_deviation, sample_size)
The formula assumes the population standard deviation is known. If not, you can just use a sample_size ≥31, calculate the sample standard deviation, and use it. This gives a pretty good approximation (see yesterday’s post).
The CONFIDENCE() formula gives the margin of error for the confidence interval. To get the actual lower and upper bounds, you both subtract and add its output to the sample mean.
Imagine an exam written by 706 students. A sample of 42 papers reveals a mean grade of 67.3 and standard deviation 12.4. Give a 95% confidence interval for the mean exam mark.
The confidence level is 95% = 0.95, so the first parameter is 1-0.95=0.05.
In a cell, key
=confidence(0.05, 12.4, 42)
Hopefully, you obtain the output 3.75, which means the confidence interval for the mean is given by
63.55 to 71.05
Apparently the mean, with 95% confidence, is between 63.55 and 71.05.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.