You have been told that 23 grouse hunters from a certain part of the Lowlands had a total catch of 111 grouse in a single day, and concluded that the catch rate there was \(\lambda_{\text {Lowlands }} \sim \gamma_{(111,23)}\). You have now spoken to 8 hunters from the Highlands, and their catch on the same day was 65 grouse. Use a neutral prior and find the posterior probability distribution for \(\lambda_{\text {Highlands }}\). Then decide, with significance \(\alpha=0.1\), whether \(H_{1}: \lambda_{\text {Highlands }}>\lambda_{\text {Lowlands }}\).