The critical value for a \( 90 \% \) confidence interval is what number to three decimal places? Type your answer... Previous

For a \( 90\% \) confidence interval, the critical value corresponds to the \( z \)-score that captures the middle \( 90\% \) of the standard normal distribution. This leaves \( 5\% \) in each tail, so we look for the \( z \)-score at \( 0.95 \) in the standard normal table, which is approximately \( 1.645 \). To take this a step further, knowing the critical value is essential in other statistical analyses, not just for constructing confidence intervals. For instance, it can be used in hypothesis testing to determine whether to reject the null hypothesis. The beauty of statistics lies in its applicability across various fields – from medicine to economics, understanding how to interpret these values opens doors to deeper insights!