What is the relationship between sample size and the width of the confidence interval?

What is the relationship between sample size and the width of the confidence interval?

• A. Increased sample size typically narrows the interval
• B. Sample size has no impact on the interval width
• C. Increased sample size widens the interval
• D. Sample size only affects the margin of error

Answer: (A)

The relationship between sample size and the width of the confidence interval is such that increasing the sample size typically results in a narrower interval. This is because a larger sample size provides more information about the population, which reduces the variability of the sample mean. As the sample size increases, the standard error of the mean (which is the standard deviation of the sample distribution divided by the square root of the sample size) decreases. Since the confidence interval is calculated using the standard error, a smaller standard error means that the interval around the estimate of the population parameter becomes narrower. A narrower confidence interval indicates that we have a more precise estimate of the true population parameter, which is desirable in statistical analysis. This inverse relationship is a fundamental concept in statistical inference and highlights the importance of obtaining larger samples to improve the accuracy of estimates.

The relationship between sample size and the width of the confidence interval is such that increasing the sample size typically results in a narrower interval. This is because a larger sample size provides more information about the population, which reduces the variability of the sample mean. As the sample size increases, the standard error of the mean (which is the standard deviation of the sample distribution divided by the square root of the sample size) decreases. Since the confidence interval is calculated using the standard error, a smaller standard error means that the interval around the estimate of the population parameter becomes narrower.

A narrower confidence interval indicates that we have a more precise estimate of the true population parameter, which is desirable in statistical analysis. This inverse relationship is a fundamental concept in statistical inference and highlights the importance of obtaining larger samples to improve the accuracy of estimates.