The director of research and development is testing a new drug. She wants to know if there is evidence at the $0\mathrm{.}05$ level that the drug stays in the system for more than $397$ minutes. For a sample of $10$ patients, the average time the drug stayed in the system was $406$ minutes with a standard deviation of $20.$ Assume the population distribution is approximately normal. Step $1$ of $3$ : State the null and alternative hypotheses.