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Hypothesis Test for How Many Houses in Southern California are Built with Pools

For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of 127 houses built in Southern California between 1950 and 1985 and an independent,random sample of 95 houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained 48 houses with pools, and the sample of houses built from 1992-present contained 31 houses with pools. Based on this survey, can we conclude, at the 0.1 level of significance, that the proportion p1 of all Southern California houses built in 1950-1985 that were built with pools is greater than the proportion p2 of all Southern California houses built from 1992-present that were built with pools?

Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.
The null hypothesis is:
The alternative hypothesis is:
Type of Test Statistic is:
The value of the Test Statistic is (Round 3 decimal places):
The p value (Round 3 decimal places):
Can you conclude that the independent portion of S California houses built with pools from 1950-1985 is greater than the proportion from 1985-present (yes or no)?

Solution Summary

A one-tailed test is conducted to find how many houses in Southern California is built with a pool.