Final answer:
The one-sample t confidence interval and the matched-pairs t confidence interval computed from related pairs of variables will yield different confidence intervals due to different methodologies, sample sizes, and confidence levels. The variability within the sample and the confidence level decided upon influences the margin of error and the width of the intervals.
Step-by-step explanation:
The question concerns whether a one-sample t confidence interval computed from a sample of pairwise differences and the matched-pairs t confidence interval computed from the pair of related variables, obtained for each individual sampled, will yield identical confidence intervals. The correct answer is b) Will yield different confidence intervals due to different methodologies. This is because while both methods involve calculating confidence intervals from paired data, the specific calculations and the manner in which data is paired can result in different confidence intervals. Furthermore, differences in sample sizes, confidence levels, and other factors such as variability can influence the margin of error and the width of confidence intervals.
When constructing confidence intervals for matched or paired samples data, it's crucial to consider the sample size and the confidence level chosen. For smaller samples, there is more variability, and the intervals tend to be wider to accommodate this uncertainty. Conversely, with larger samples, the confidence intervals tend to be narrower, reflecting less variability and giving a more precise estimate of the population parameter. A 99 percent confidence interval will be wider than a 95 percent confidence interval because it aims to include a larger proportion of the population.
In conclusion, different methodologies, sample sizes, and confidence levels will impact the estimated intervals, leading to potentially different confidence intervals for a one-sample t statistic and a matched-pairs statistic.