Which of the following factors does not usually affect the width of a confidence interval?

The correct answer is - Population size

Key Points

• Population size
  • Confidence intervals are typically calculated using the sample statistics rather than the size of the entire population.
  • In most practical applications, the population is considered infinitely large, making population size an irrelevant factor in determining the width of a confidence interval.
  • The finite population correction (FPC) is only applied when the sample is a significant fraction of the total population (typically >5%), which is uncommon in large populations.
• Sample size
  • Larger sample sizes result in narrower confidence intervals due to reduced standard error.
• Confidence desired
  • Higher confidence levels (e.g., 99% vs 95%) require wider intervals to ensure greater certainty of capturing the true parameter.
• Variability in the population
  • Higher variability (or standard deviation) leads to wider confidence intervals to accommodate the increased uncertainty.

Additional Information

• Formula for confidence interval width
  • For means: CI = x̄ ± Z*(σ/√n)
  • Key variables affecting width:
    • Z*: Depends on the confidence level.
    • σ: Population standard deviation (variability).
    • n: Sample size.
• Finite Population Correction (FPC)
  • Used only when the sample is a large proportion of the population.
  • FPC = √((N - n)/(N - 1)), where N = population size, n = sample size.
  • In most exam scenarios, FPC is negligible, so population size does not affect confidence interval width.
• Common misconceptions
  • Assuming that a larger population always increases uncertainty — this is incorrect unless FPC is applied.
  • Believing population size directly affects width — in standard practice, it does not.