Setting Up Tests for Population Mean Practice Test

A city’s water department states that the mean lead concentration in tap water is 5 parts per billion (ppb). A public health researcher wants to check whether the true mean lead concentration is different from 5 ppb. A random sample of 50 homes is tested, and the sample mean lead concentration is 5.8 ppb. Which hypotheses are appropriate for a one-sample test of a population mean lead concentration?

A city transit agency reports that the mean wait time for a bus on a certain route is 12 minutes. A commuter advocacy group randomly samples $n=35$ bus arrivals and records wait times, obtaining a sample mean of $\bar{x}=13.1$ minutes. The group wants to test whether the true mean wait time is different from 12 minutes. Which hypotheses are appropriate?