What is the basic relationship between sample size and precision?

What is the basic relationship between sample size and precision?

• A. Larger sample size typically increases precision, reducing the width of the confidence interval.
• B. Larger sample size reduces precision.
• C. Sample size has no effect on precision.
• D. Precision depends only on data variability.

Answer: (A)

Precision is about how close your estimate is to the true value, and it’s reflected in how narrow the confidence interval is. As you gather more data, the sampling error shrinks because the standard error of the estimate decreases roughly in proportion to 1 over the square root of the sample size. Since the confidence interval is built from that standard error, increasing the sample size makes the interval narrower, giving a more precise estimate. Doubling the sample size doesn’t double precision; it reduces the standard error by about a factor of sqrt(2), with diminishing returns as the sample grows. While data variability affects how wide the interval starts out, the key effect of increasing sample size is to reduce precision error through the standard error, so larger samples lead to more precise estimates.

Precision is about how close your estimate is to the true value, and it’s reflected in how narrow the confidence interval is. As you gather more data, the sampling error shrinks because the standard error of the estimate decreases roughly in proportion to 1 over the square root of the sample size. Since the confidence interval is built from that standard error, increasing the sample size makes the interval narrower, giving a more precise estimate. Doubling the sample size doesn’t double precision; it reduces the standard error by about a factor of sqrt(2), with diminishing returns as the sample grows. While data variability affects how wide the interval starts out, the key effect of increasing sample size is to reduce precision error through the standard error, so larger samples lead to more precise estimates.