The 99% confidence interval of Becky's muffins' weights is the range of 121 to 139 g. And so, when selling muffins, she can be 99% sure that any muffin she baked weighs between 121 and 139 g. But 1% of the time, she might accidentally produce a chonky muffin (or a tiny one!) Procedure to find the bootstrap confidence interval for the mean. 1. Draw N samples ( N will be in the hundreds, and if the software allows, in the thousands) from the original sample with replacement. 2. For each of the samples, find the sample mean. 3. A 95% confidence interval for the population mean is {eq}(\$57,161.32, \$57,338.68) {/eq}. Example 2. A teacher wants to estimate the mean height of all 400 students at her school. She takes a A point estimate is a single number. Whereas, a confidence interval, naturally, is an interval. The two are closely related. In fact, the point estimate is located exactly in the middle of the confidence interval. However, confidence intervals provide much more information and are preferred when making inferences. The z-score for a 98-percent confidence interval is 2.807, meaning that 98 times out of a hundred trials, the sample has a 98% confidence level. This value is the 99.5th percentile of the standard normal distribution. This means that the sample’s mean and standard deviation do not have an impact on the width of the confidence interval. 95%. 1.96. 90%. 1.645. 80%. 1.28. Table A.1: Normal Critical Values for Confidence Levels. 12.2: Normal Critical Values for Confidence Levels is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Kathryn Kozak via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit Taking the exponent of the upper and lower confidence limits will give you the confidence interval for the risk ratio. RR = eln(RR) R R = e l n ( R R) You can convert the risk ratio into your original question of percent reduction (assuming the risk ratio is less than 1) with the following. A confidence interval of 95 signifies that in a sample or population analysis, 95% of the true values would provide the same mean value—even if the statistical test is repeated multiple times using different sample sets. In other words, we can say that there is a 95% probability that the true population mean lies between the lower and the mUnnihY.