This would be the hypothesis to use for independent chi square testing.
Pools have always been a fun amenity to have when it comes to owning a home. However, the cost associated with having a pool can help a homeowner determine if they want a pool or not. Two townships, within the Denver, Colorado area, were looked at to see if having a pool in one's backyard is still a popular item.
However, if you wish to implement a proposal to show whether a home has a pool or not in the township the house is located, then the team essentially will develop a 5 x 2 contingency table, based on the township variable (5 townships) and the pool variable ( 0 meaning no pool, and 1 meaning pool exists). Here the team has access to all 105 observations in the data set, rather than just looking at two townships. The more data, the higher the accuracy of results obtained.
Can set a level of significance of 0.05, and at this level o significance conduct the contingency table analysis.
In this problem two significance tests, testing independence of characteristics and testing of proportion, are done. Detailed procedure for the conduct of these two tests is given in the solution. Calculations are provided in the attached excel sheet.