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, thatpractice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 138 houses built in SouthernCalifornia in the twentieth century and an independent, random sample of 84 new houses built in Southern California. The sample of twentieth century housescontained 47 houses with pools, and the sample of new houses contained 27 houses with pools.Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion P, of all Southern California twentieth century houses that were builtwith 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 offormulas.)(a) State the null hypothesis H, and the alternative hypothesis H1.H, :0H :0(b) Determine the type of test statistic to use.(Choose one)D=0OSOO20(c) Find the value of the test statistic. (Round to three or more decimal places.)O 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, thatpractice may be changing, possibly as a measure to help reduce climate change. A recent study examined a random sample of 138 houses built in SouthernCalifornia in the twentieth century and an independent, random sample of 84 new houses built in Southern California. The sample of twentieth century housescontained 47 houses with pools, and the sample of new houses contained 27 houses with pools.Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion p, of all Southern California twentieth century houses that were builtwith 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 offormulas.)(a) State the null hypothesis H, and the alternative hypothesis H,.H, :0H, :0믐(b) Determine the type of test statistic to use.Choose one)O=0OSO(c) Fttest statistic. (Round to three or more decimal places.)O

Question

Accepted Answer

Solution:
Given information:
n1= 138n2= 84x1=…