Final answer:
The lower limit can be determined by subtracting the range from the upper limit. Answer choice A is correct, as this method accounts for the error bound within confidence intervals. Other choices involving the standard deviation apply to different contexts.
Step-by-step explanation:
The algebraic expression for the lower limit can be determined by using the upper limit and the range of the confidence interval. To find the lower limit, we subtract the range from the upper limit. In the context of confidence intervals and statistics, the range is typically defined as the difference between the upper and lower bounds, or sometimes as the error bound. If the range or error bound is not directly given, it may be represented by the standard error or a multiple of the standard deviation, depending on the data and the calculations being performed.
For example, if you are given the upper limit of a confidence interval and the error bound, you can find the lower limit by subtracting the error bound from the upper limit. Similarly, if you have the upper limit and the range (which is double the error bound), you subtract the range from the upper limit and divide by 2 to find the error bound, and then subtract it from the upper limit to get the lower limit. These procedures would correspond to answer choice A. Answer choices C and D suggest adding or subtracting the standard deviation, which might be correct in different contexts, such as when calculating values around the mean in a normal distribution, but not for directly finding the lower limit of a confidence interval.
When comparing the sample mean and sample standard deviation to theoretical values, these metrics help us understand how our sample relates to the overall population and whether there might be any outliers or unusual data points. Understanding these concepts is crucial when interpreting statistical data and drawing conclusions.