Final answer:
The number of standard deviations for confidence limits in laboratories depends on the desired confidence level. Typically, a 90% confidence interval requires 1.645 standard deviations, while a 95% interval requires about 1.96 standard deviations. When the population standard deviation is unknown and the sample size is small, a t-distribution is used.
Step-by-step explanation:
Laboratories and other disciplines that rely on statistical analysis often use confidence intervals to estimate a population parameter with a specified level of certainty. The confidence limit they should meet is determined by the desired confidence level. Confidence intervals incorporate the sample standard deviation (as an estimate of the population standard deviation) to calculate the range in which we believe the true population parameter will fall.
For example, to construct a 90 percent confidence interval, you would use a critical value of 1.645, which corresponds to 1.645 standard deviations from the mean in a standard normal distribution. This would capture the central 90 percent of the probability. In comparison, a higher confidence level, such as 95 percent, requires a wider interval (about 1.96 standard deviations from the mean) because it is designed to capture more of the distribution's area.
When the standard deviation is unknown and the sample size is small, statisticians use a t-distribution instead of a normal distribution to adjust for the additional uncertainty. The number of standard deviations used in the calculation depends on the confidence level and, in the absence of the population standard deviation, the sample standard deviation. Overall, no single 'correct' number of standard deviations applies to all confidence levels; it is always tied to the confidence level one wants to achieve. The more certain you want to be about the interval containing the actual population mean, the wider (more standard deviations) the interval will be.