Suppose that you are the manager of T.C. Resort Properties, a collection of five upscale resort hotels located on two resort islands. On one of the islands, T.C. Resort Properties has two hotels, the Beachcomber and the Windsurfer. In tabulating the responses to the single question, "Are you likely to choose this hotel again?" 163 of 227 guests at the Beachcomber responded yes, and 154 of 262 guests at the Windsurfer responded yes. At the 0.05 level of significance, is there evidence of a significant difference in guest satisfaction (as measured by the likelihood to return to the hotel) between the two hotels?
What would be the proper set of hypotheses?
H0: π1 - π2 = 0; H1: π1 - π2 ≠ 0