What is the critical value \( z^{*} \) for constructing a \( 95 \% \) confidence interval? Choose 1 answer: (A) \( z^{*}=1.282 \) (B) \( z^{*}=1.645 \) (C) \( z^{*}=1.96 \) (D) \( z^{*}=2.576 \)

To construct a \( 95\% \) confidence interval, you want to account for the central area of the standard normal distribution that corresponds to that confidence level. This includes \( 95\% \) of the area in the middle, leaving \( 5\% \) in the tails, with \( 2.5\% \) in each tail. The critical value \( z^{*} \) that corresponds to this is indeed \( 1.96 \), making option (C) the correct answer. When you consider confidence intervals in Statistics, you're essentially creating a safety net around your estimates, helping you understand how much uncertainty is inherent in your sample data. By using \( z^{*} \), you define the "stretch" of that net! So next time you’re calculating an interval, think of it as a cozy blanket that protects you from wild fluctuations in data. Remember, a little margin of error goes a long way in ensuring your findings hold up!