Mean hemoglobin of a sample of 100 pregnant women was found to be 10 mg% with a standard error of 1.0 mg%. The standard error of the estimate would he
## **Core Concept**
The standard error (SE) of a sample statistic, such as the mean, measures the variability or dispersion of that statistic across different samples from the same population. In this context, we're dealing with the standard error of the mean (SEM) of hemoglobin levels in pregnant women. The formula for the standard error of the mean is (SEM = frac{sigma}{sqrt{n}}), where (sigma) is the population standard deviation and (n) is the sample size.
## **Why the Correct Answer is Right**
Given that the standard error (SE) of the mean hemoglobin level is 1.0 mg%, and the sample size ((n)) is 100, we can use the formula for the standard error of the mean to find the standard deviation ((sigma)) of the sample, which is often considered an estimate of the population standard deviation. The formula can be rearranged as (sigma = SEM times sqrt{n}). Substituting the given values: (sigma = 1.0 times sqrt{100} = 1.0 times 10 = 10) mg%. The standard error of the estimate of the mean (or simply put, the standard error of the mean) is already provided as 1.0 mg%, which directly corresponds to option .
## **Why Each Wrong Option is Incorrect**
- **Option A:** This option does not match any standard formula related to standard error or standard deviation directly.
- **Option B:** This seems to misinterpret or misrepresent the relationship between standard error, sample size, and standard deviation.
- **Option C:** This option might seem plausible but does not correctly represent the calculation or concept related to the standard error of the estimate in this context.
## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the standard error of the mean (SEM) decreases as the sample size ((n)) increases, according to the formula (SEM = frac{sigma}{sqrt{n}}). This implies that larger samples provide more precise estimates of the population mean. For clinical research, understanding the precision of sample estimates is crucial for interpreting results and making inferences about the population.
## **Correct Answer:** .