Question

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

161

houses built in Southern California between 1950 and 1985 and an independent, random sample of

80

houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained

72

houses with pools, and the sample of houses built from 1992-present contained

32

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:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF
The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.1 level of significance: (Round to at least three decimal places.)
Can we conclude that the proportion of Southern California houses built with pools from 1950-1985 is greater than the proportion from 1985-present?		Yes	No

Answer 1

p1 of all Southern California houses built in 1950-1985 with pools
s = 72
n = 161

p2 houses built from 1992-present that were built with pools
s=32
n= 80

Hypothesis

Type of test statistic : z statistic

Test statistic : 0.697

critical value : 1.28

Can we conclude that the proportion of Southern California houses built with pools from 1950-1985 is greater than the proportion from 1985-present? No

Detailed hypothesis