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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 159 houses built in Southern California in the twentieth century and an independent random sample of 67 new houses built in Southern California The sample of twentieth century houses contained 78 houses with pools and the sample of new houses contained 29 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 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 H Ho O H b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places d Find the critical value at the 0 05 level of significance Round to three or more decimal places e Can we conclude that the proportion of Southern California twentieth century houses built with pools is greater than the proportion for new homes Yes No x X 0 a X S p 0 0 OSO 020 O Q olo

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