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 71 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 – 1985 contained 43 houses with pools, and the sample of houses built from 1992 – present contained 23 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 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 complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the value of the test statistic. Round to three or more decimal places. c. Find the critical value at the 0.05 level of significance. Round to three or more decimal places. d. Can we conclude
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 71 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 – 1985 contained 43 houses with pools, and the sample of houses built from 1992 – present contained 23 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 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 complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below.
a. State the null hypothesis H0 and the alternative hypothesis H1.
b. Find the value of the test statistic. Round to three or more decimal places.
c. Find the critical value at the 0.05 level of significance. Round to three or more decimal places.
d. Can we conclude that the proportion of Southern California houses built with pools from 1950 – 1985 is greater than the proportion from 1985 – present?
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