A researcher claims that more than $40\%$ of adults prefer drinking coffee over tea. To test this claim, a random sample of $100$ adults is surveyed, and $47\%$ report preferring coffee. Using a significance level of $\alpha =0.01$, determine the critical value $z_{\text{crit}}$, and decide whether to reject or fail to reject the null hypothesis.

• A. $z_{\text{crit}}=1.96$Reject $H_0$
• B. $z_{\text{crit}}=2.33$Fail to reject $H_0$
• C. $z_{\text{crit}}=1.64$Fail to reject $H_0$
• D. $z_{\text{crit}}=1.09$Reject $H_0$

Answer: (B)