S.D. is 1.96 the confidence limit is –
**Core Concept**
The confidence interval (CI) is a statistical measure that provides a range of values within which a population parameter is likely to lie. It is calculated from a sample of data and is used to estimate the precision of a sample statistic. In this context, a confidence limit is a critical value of the test statistic that marks the boundary of the confidence interval.
**Why the Correct Answer is Right**
SD (Standard Deviation) is used to calculate the margin of error, which is the width of the confidence interval. The formula to calculate the confidence interval is: CI = sample mean ± (Z * (SD / √n)), where Z is the Z-score corresponding to the desired confidence level. For a 95% confidence level, the Z-score is approximately 1.96. This means that if the sample mean is within 1.96 standard deviations of the true population mean, there is a 95% chance that the true population mean lies within this interval.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is not relevant to the calculation of the confidence limit, and does not provide any information about the confidence interval.
**Option B:** This option is incorrect because the Z-score for a 95% confidence level is not 1.65, but rather 1.96.
**Option C:** This option is incorrect because the Z-score for a 95% confidence level is not 2.58, but rather 1.96.
**Option D:** This option is not relevant to the calculation of the confidence limit, and does not provide any information about the confidence interval.
**Clinical Pearl / High-Yield Fact**
When interpreting confidence intervals, remember that a wider interval indicates less precision in the estimate, while a narrower interval indicates more precision.
**Correct Answer:** 1.96.