To calculate the margin of error for a 95% confidence interval for the population mean, we can use the following formula:
Margin of error = z-score x standard deviation / sqrt(sample size)
where z-score is a value from the standard normal distribution that corresponds to the desired confidence level (in this case, 95%), and standard deviation is the population standard deviation (which you provided as 8.26).
First, we need to find the z-score. Using a standard normal distribution table or calculator, we can find that the z-score for a 95% confidence level is approximately 1.96.
Now, we can plug in the values to the formula:
Margin of error = 1.96 x 8.26 / sqrt(17)
Simplifying and calculating the value, we get:
Margin of error = 1.96 x 8.26 / sqrt(17) ≈ 3.53
Therefore, the margin of error for a 95% confidence interval for the population mean, based on a sample of 17 members, is approximately 3.53.
It's important to note that this calculation assumes that the sample is randomly drawn from the population, and that the population is normally distributed. If these assumptions are not met, the margin of error may not be accurate.