Discussion:
Hypothesis test for the difference of population proportions
Q: 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 143 houses built in Southern California between 1950 and 1985 and an independent, 82 random sample of houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained 53 houses with pools, and the sample of houses built from 1992-present contained 24 houses with pools. Based on this survey, can we conclude, at 0.01 the level of significance, that the proportion ρ1 of all Southern California houses built in 1950-1985 that were built with pools is greater than the proportion ρ2 of all Southern California houses built from 1992-present that were built with pools?
Perform a one-tailed test.
The null hypothesis:
The alternate hypothesis:
The type of test statistic: (Z, t, Chi square, or F?)
The value of the test statistic:
The critical value: