A recent study estimated the mean cholesterol level for adult males over a certain age using a random sample of 10 men, finding a sample mean of 242 mg/dL.
Key points about this study and sample size:
- The sample size (n = 10) is quite small. Small sample sizes can still be used for statistical inference, but they generally provide less precise estimates and wider confidence intervals compared to larger samples
- The sample mean of 242 mg/dL is an estimate of the population mean cholesterol level. Because the sample is random, this mean is an unbiased estimator, but with only 10 men, the estimate may have considerable variability
- To assess the reliability of this estimate, one would typically calculate the standard error of the mean, which depends on the sample standard deviation and the sample size. With small n, the standard error is larger, reflecting greater uncertainty
- For more precise estimation or hypothesis testing, larger samples (e.g., n ≥ 30 or more) are usually recommended to better approximate the population mean and reduce sampling variability
- If the population standard deviation is known or estimated, one can construct confidence intervals around the sample mean to quantify the uncertainty. The formula for the confidence interval width and required sample size involves the standard deviation, desired confidence level (Z-score), and margin of error
Summary
The study's sample mean cholesterol of 242 mg/dL from 10 men provides an initial estimate but is limited by the small sample size, which increases uncertainty in the estimate. Larger samples would yield more reliable and precise estimates of the population mean cholesterol level for adult males over the specified age
