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In the twentieth century, it was a common practice in Southern California for houses to be built with pools in the backyard. For new homes, however, that practice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 161 houses built in Southern California in the twentieth century and an independent, random sample of $2 new houses built in Southern California. The sample of twentieth century houses contained 71 houses with pools, and the sample of new houses contained 22 houses with pools. Based on this survey, can we conclude, at the 0.01 level of significance, that the proportion p, of all Southern California twentieth century houses that were built with pools is greater than the proportion p, of all new Southern California houses that were built with pools? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis #1. O P Ho : 1 5 H : 1 (b) Determine the type of test statistic to use. (Choose one) 0-0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0=0 0 0 0>0 X 5 (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) 0 (e) Can we conclude that the proportion of Southern California twentieth century houses built with pools is greater than the proportion for new homes? OYes ONo