A meteorologist claims that the median daily high temperature for the month of July in Pittsburgh is \(83^{\circ}\) Fahrenheit. The high temperatures (in degrees Fahrenheit) for 15 randomly selected July days in Pittsburgh are listed below. At \(\alpha=0.01\), is there enough evidence to reject the meteorologist's claim? (Adapted from U.S. National Oceanic and Atmospheric Administration)

\[ \begin{array}{lllllllllllllll} 74 & 79 & 81 & 86 & 90 & 79 & 81 & 83 & 81 & 74 & 78 & 76 & 84 & 82 & 85 \end{array} \]

(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, and

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