Here's how we approach this question in a step-by-step method:
Step 1:
We first need to calculate the degrees of freedom. This value is essentially the number of independent ways by which a dynamic system can move, without violating any constraint imposed on it. In this case, the degrees of freedom are calculated easily as the sample size minus one, so with a sample size of 17, the degrees of freedom will be 17 - 1 = 16.
Step 2:
Next, we need to calculate the t-critical value. To do this, we need the degrees of freedom (which we just calculated) and the confidence level of our experiment. Here, the confidence level is 99% (0.99 as a decimal). Using these two values, with the degrees of freedom as input to the t-distribution function, we find that the t-critical value is approximately 2.9207816223499967.
Step 3:
Third step involves figuring out the standard error. The standard error can be estimated by dividing the standard deviation (which is 7.1 minutes here) by the square root of the sample size (which is 17). Unless you have a strong mathematical background, it is nearly impossible to do this mentally or by hand, you would use a calculator or computer to do this. The standard error in this case is roughly 1.7220029377579642.
Step 4:
The final step in this process is to calculate the margin of error. The margin of error is calculated by multiplying t-critical value by the standard error. Thus, the margin of error will be approximately 5.029594534236167 minutes.
So, to answer your question, the margin of error for the population mean is about 5.03 minutes. It's important to remember that this margin of error is a part of the 99% confidence interval for the population mean which means we can affirm that we are 99% confident that the real population mean falls within +/- 5.03 minutes of our sample mean.