Final answer:
To find the upper and lower bounds of a confidence interval, subtract the error bound from the upper limit if you have the sample mean, or if not known, average the upper and lower limits. The error bound variance is affected by sample size and confidence level.
Step-by-step explanation:
To find the upper bound and the lower bound of a confidence interval, you can use the given sample mean and the error bound (EBM). If the sample mean is known, subtract the error bound from the upper limit to get the lower bound and add the error bound to the lower limit to get the upper bound. For example, if a confidence interval is (67.18, 68.82) and the sample mean is 68, the error bound can be calculated by subtracting the sample mean from the upper bound (68.82 - 68 = 0.82). Alternatively, if the sample mean is unknown, you can average the upper and lower bounds of the confidence interval (in this case, (67.18 + 68.82) / 2 = 68), which would give you the sample mean. Then, the error bound can be found by taking half the difference between the upper and lower bounds.
When dealing with different sample sizes or confidence levels, remember that the size of the error bound will vary. A higher confidence level will result in a larger error bound, while a larger sample size will reduce it. According to the central limit theorem, the EBM can be affected by the sample size and the desired level of confidence.