(Solved): i. A restaurant owner wishes to estimate, to within 55 seconds, the mean time taken to serve food t ...

i. A restaurant owner wishes to estimate, to within 55 seconds, the mean time taken to serve food to customers with \( 99 \% \) confidence. In the past, the standard deviation of serving time has been about \( 2.5 \) minutes. Estimate the minimum size of the sample required. ii. The restaurant owner wishes to estimate the mean time taken to serve food to customers with \( 99 \% \) confidence with a margin of error \( E=0.5 \) minutes given that \( \sigma=2.5 \) minutes. Estimate the minimum size of the sample required. iii. Which of the following statements is true when comparing the two required sample sizes? (Hint: In part i., the margin of error \( \mathrm{E}=55 / 60 \) minutes. Round up the final answer.)