Question 1 of 10, Step 1 of 1 \( \begin{array}{l}\text { What happens to the width of a confidence interval for a population mean if the level of confidence is } \\ \text { increased without changing the sample size? Assume that the population standard deviation is } \\ \text { unknown and the population distribution is approximately normal. } \\ \text { Select your answer from the choices below. }\end{array} \) Answer Correct

When you increase the level of confidence, the critical value from the t-distribution becomes larger, which in turn increases the width of the confidence interval. This means you're widening the interval to be more confident that it captures the true population mean, but achieving that comes at the cost of less precision. In practical terms, if you're going for a 99% confidence interval instead of a 95%, you’re saying, "I want to be more sure that I'm right," which means you’re opening up your interval, maybe even like widening your stance in a three-legged race! So, while you might feel more assured in your results, they may not be as pinpoint accurate.