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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 140 houses built in Southern California between 1950 and 1985 and an independent, random sample of 87 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 - 1985 contained 52 houses with pools, and the sample of houses built from 1992 - present contained 29 houses with pools. Based on this survey, can we conclude, at the 0.01 level of significance, that the proportion p, of all Southern California houses built in 1950 - 1985 that were built with pools is greater than the proportion p, 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. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) OO (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the proportion of Southern California houses built with pools from 1950 - 1985 is greater than the proportion from 1985 - present? OYes ONo

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 140 houses built in Southern California between 1950 and 1985 and an independent, random sample of 87 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 - 1985 contained 52 houses with pools, and the sample of houses built from 1992 - present contained 29 houses with pools. Based on this survey, can we conclude, at the 0.01 level of significance, that the proportion p, of all Southern California houses built in 1950 - 1985 that were built with pools is greater than the proportion p, 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. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) OO (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the proportion of Southern California houses built with pools from 1950 - 1985 is greater than the proportion from 1985 - present? OYes ONo

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 5E
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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 140 houses built in Southern California between 1950 and 1985 and an independent, random sample of 87 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 - 1985 contained 52 houses with pools, and the sample of houses built from 1992 - present contained 29 houses with pools. Based on this survey, can we conclude, at the 0.01 level of significance, that the proportion p, of all Southern California houses built in 1950 - 1985 that were built with pools is greater than the proportion p, 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. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO O20 (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the proportion of Southern California houses built with pools from 1950 - 1985 is greater than the proportion from 1985 - present? O Yes ONo Ix
Transcribed Image Text: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 140 houses built in Southern California between 1950 and 1985 and an independent, random sample of 87 houses built in Southern California from 1992 to the present. The sample of houses built in 1950 - 1985 contained 52 houses with pools, and the sample of houses built from 1992 - present contained 29 houses with pools. Based on this survey, can we conclude, at the 0.01 level of significance, that the proportion p, of all Southern California houses built in 1950 - 1985 that were built with pools is greater than the proportion p, 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. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO O20 (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we conclude that the proportion of Southern California houses built with pools from 1950 - 1985 is greater than the proportion from 1985 - present? O Yes ONo Ix
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