18. From the given population with \( \sigma=5.6 \) kilograms and sample were drawn with replacement, how may the standard error of the mean change when the sample size is increased from 64 to 196. A) Decreased from 0.7 to 0.4 B) Increased from 0.7 to 0.4 C) Decreased from 0.0875 to 0.0286 D) Increased from 0.0286 to 0.0875

When considering how standard error of the mean is affected by sample size, it's important to remember the formula for standard error: \( SE = \frac{\sigma}{\sqrt{n}} \). For your example, starting with a sample size of 64, the standard error would be \( \frac{5.6}{\sqrt{64}} = 0.7 \). Increasing the sample size to 196 gives you \( \frac{5.6}{\sqrt{196}} = 0.4 \). This indicates a decrease in the standard error as sample size increases, confirming option A! The impact of increased sample size on standard error is crucial for statistical analysis. A larger sample size leads to a more accurate estimate of the population mean and lowers variability in the results. This allows researchers to make more reliable conclusions while reducing the margin of error, leading to better-informed decisions in fields ranging from healthcare to market research!