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 160 houses built in Southern California in the twentieth century and an independent, random sample of 88 new houses built in Southern California. The sample of twentieth century houses contained 74 houses with pools, and the sample of new houses contained 38

houses with pools. Based on this survey, can we conclude, at the 0.05 level of significance, that the proportion

p1 of all Southern California twentieth century houses that were built with pools is greater than the proportion p2

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.)

Questions

Find the value of the test statistic. (Round to three or more decimal places.)

Find the p-value, Round to three or more decimal places