The Environmental Protection Agency (EPA) sets a standard for arsenic levels in water to be no more than 10 ppb (parts per billion). You suspect that, on average, arsenic levels in your community's water are much higher than this standard. You will study this by measuring arsenic levels in water samples selected from 15 households and testing H0: μ = 10 ppb versus HA: μ > 10 ppb, where μ denotes the mean arsenic level (ppb) in your community.
(a) Describe the Type I and Type II errors that could be made in this study and the practical consequences of making these types of errors.
(b) You gather your sample, compute the sample mean and standard deviation, then have your intern carry out the one-sample test for a mean. He uses the standard normal distribution instead of the t distribution and claims to reject the null hypothesis. If you had used the t distribution, would you have necessarily come to the same conclusion? Explain.