A real estate agent claims that the median sales price of new privately owned one-family homes sold in a recent month is \(\$ 253,000\) or less. The sales prices (in dollars) of 10 randomly selected homes are listed below. At \(\alpha=0.05\), is there enough evidence to reject the agent's claim? (Adapted from National Association of Realtors)

\[ \begin{array}{lllll} 262,600 & 300,100 & 269,200 & 249,400 & 183,400 \\ 253,500 & 325,600 & 223,500 & 241,300 & 271,300 \end{array} \]

(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.