During a weather report, a meteorologist claims that the median daily high temperature for the month of January in San Diego is \(66^{\circ}\) Fahrenheit. The high temperatures (in degrees Fahrenheit) for 16 randomly selected January days in San Diego are listed below. At \(\alpha=0.01\), can you reject the meteorologist's claim? (Adapted from U.S. National Oceanic and Atmospheric Administration)

\[ \begin{array}{llllllllllllllll} 78 & 74 & 72 & 72 & 70 & 70 & 72 & 78 & 74 & 71 & 72 & 74 & 77 & 79 & 75 & 73 \end{array} \]

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value,

(c) find the test statistic,

(d) decide whether to reject or fail to reject the null hypothesis,

(e) interpret the decision in the context of the original claim.