Problem
According to a report, the standard deviation of monthly cell phone bills was $\$ 4.85$ in 2017 . A researcher suspects that the standard deviation of monthly cell phone bills is different today. What would it mean to make a Type I error? A. The sample evidence did not lead the researcher to believe the standard deviation of monthly cell phone bills is different from $\$ 4.85$ when, in fact, the standard deviation of bills is different from $\$ 4.85$. B. The sample evidence did not lead the researcher to believe the standard deviation of monthly cell phone bills is higher than $\$ 4.85$ when, in fact, the standard deviation of bills is higher than $\$ 4.85$. C. The sample evidence led the researcher to believe the standard deviation of monthly cell phone bills is higher than $\$ 4.85$ when, in fact, the standard deviation of bills is $\$ 4.85$. D. The sample evidence led the researcher to believe the standard deviation of monthly cell phone bills is different from $\$ 4.85$ when, in fact, the standard deviation of bills is $\$ 4.85$.
Solution
Step 1 ：A Type I error, also known as a false positive, occurs when we reject a true null hypothesis. In this context, the null hypothesis is that the standard deviation of monthly cell phone bills is still $4.85.
Step 2 ：Therefore, a Type I error would occur if the researcher concludes that the standard deviation is different from $4.85 when it is actually still $4.85.
Step 3 ：\(\boxed{\text{D. The sample evidence led the researcher to believe the standard deviation of monthly cell phone bills is different from \$4.85 when, in fact, the standard deviation of bills is \$4.85.}}\)
