A government agency claims that the median sentence length for all federal prisoners is 2 years. In a random sample of 180 federal prisoners, 65 have sentence lengths that are less than 2 years, 109 have sentence lengths that are more than 2 years, and 6 have sentence lengths that are 2 years. At \(\alpha=0.10\), can you reject the agency's claim?

Use a sign test to test the claim by doing the following.

(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.