Question: Suppose a personal water craft (PWC) manufacturer wants to compare the potential market for its products in the northeastern United States to the market in the southeastern United States. Such a comparison would help the manufacturer decide where to concentrate sales efforts. Using telephone directories, the company randomly chooses 1000 households in the southeast (SE) and 1000 households in the northeast (NE) and determines whether each household plans to buy a PWC within the next 5 years. 42 households in the SE and 24 households in the NE indicated they will purchase a PWC within 5 years. The objective is to use this sample information to make an inference about the difference ( \[{{p}_{1}}-{{p}_{2}}\] ) between the proportion \[{{p}_{1}}\] of all households in the SE and the proportion \[{{p}_{2}}\] of all households in the NE that plan to purchase a PWC within 5 years. Complete the study for the company. Assume all statistical requirements are satisfied.