Final answer:
The margin of error, e, for the given confidence interval (9.51, 13.23) is 1.86. This is calculated by taking the difference between the upper and lower bounds of the interval, dividing by 2, and is reflective of the precision with which we estimate the population mean.
Step-by-step explanation:
The question is asking to calculate the margin of error from a given confidence interval for a population mean. The provided confidence interval is 9.51 < μ < 13.23, where μ represents the population mean.
To calculate the margin of error, e, we take the upper bound of the confidence interval and subtract the lower bound, and then divide by 2. This represents half the length of the confidence interval. In this case, the calculation would be as follows:
(13.23 - 9.51) / 2 = 3.72 / 2 = 1.86
Therefore, the margin of error, e, is 1.86. This means that we add and subtract 1.86 from the sample mean to form the confidence interval, and this range is expected to contain the true population mean with a certain level of confidence.
It is important to note that the size of the margin of error is influenced by both the size of the sample and the variation within the sample. Moreover, the selected confidence level (e.g., 90%, 95%) will also determine the margin of error, as higher confidence levels typically result in wider intervals.