Hello there! As a domain expert in statistics, I'm here to help you understand the concept of confidence intervals and how to determine the z-value for a 99% confidence level. A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown parameter. The confidence level reflects the frequency (i.e., the proportion) of possible confidence intervals that contain the true value. For instance, a 95% confidence level implies that if we were to take all possible samples of a certain size from the population and calculate a confidence interval for each sample, then 95% of these intervals would contain the true population parameter. Now, let's talk about the z-value. In statistics, the z-value is the number of standard deviations a data point is from the mean. When we're dealing with confidence intervals, the z-value is a critical component because it helps us to define the width of the interval. Specifically, for a normal distribution, the z-value corresponds to the number of standard deviations we go out from the mean to capture a certain percentage of the data. For a 99% confidence interval, we want to capture 99% of the data around the mean. To find the z-value that corresponds to this level, we need to look at the standard normal distribution table (also known as the z-table), which lists the area to the left of a given z-value. Since we want 99% of the data, we need to find the z-value that leaves 1% in the tail (because it's a two-tailed test for confidence intervals). This means we need to find the z-value that corresponds to an area of 0.995 in the standard normal distribution. According to the standard normal distribution table, the z-value that corresponds to an area of 0.995 is approximately 2.576. This value is the one we would typically use for a 99% confidence interval in a two-tailed test. Now, let's address the reference content you provided. It seems to be a snippet from a statistics book or resource, and it lists z*-values for various confidence levels. The z*-value is a modified z-value that accounts for the fact that we're dealing with a sample rather than the entire population. However, for the purpose of finding the z-value for a 99% confidence interval, we're focusing on the standard z-value, which is approximately 2.576, not the z*-value. To summarize, for a 99% confidence interval, the z-value you would use is approximately 2.576. This value is derived from the standard normal distribution and is used to construct the confidence interval in a two-tailed test scenario. Now, let's proceed with the next steps as per your instructions. read more >>

Statistics For Dummies, 2nd EditionConfidence Levelz*-C value90%1.6495%1.9698%2.3399%2.582 more rowsread more >>