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10.27 The state of California is working very hard to ensure that all elementary age students whose native language is not English become proficient in English by the sixth grade. Their progress is monitored each year using the California English Language Development test. The results for two school districts in southern California for the 2003 school year are given in the accom- panying table. Do the data indicate a significant difference in the 2003 proportions of students who are fluent in English for the two districts? Use α = .01. District Riverside Palm Springs long Number of students tested Percentage fluent 6124 5512 40 to aid 37 10 ibu2 ES.OF Answer: PR Pp: The proportion of elementary age students in Riverside who are fluent in English The proportion of elementary age students in Palm Springs who are fluent in English Hypotheses: HA: (PR - PP) 0 vs. Ho: (PR-PP) = 0 α = 1% • is (PR-PP) • 00=0 • is (PR - PP) (0.4 0.37) 0.03 = NR = 6124, np = 5512 PRX (1-PR) • σ is Ppx (1-Pp) + PRX (1-PR) Ppx (1-pp) + nR np nR np = 0.009 Rejection region: Reject Ho: (PR-Pp) = 0 if and only if the R.S.'s (PR-Pp) value is less than -Z0.5% PRX (1-PR) + nR Bpx (1-p) Пр =-(2.58) (0.009) = -0.023 ог ⚫ greater than +0.023 Test Statistic Value: (PR - PP) Test Decision: (0.4-0.37) = 0.03 Reject the null hypothesis since the test statistic falls into the RR Px(1-P)+P(1-Pp) (PR-PP)-Z0.5% ng np 99% C.I. for (PR-PP): (PR-PP) € (PR-PP) + Z0.5% PRX (1-PR)+ Ppx (1-Pp) nR np Interpretation: (PR-PP) € ((0.03 -0.023, 0.03+0.023) = (0.7%, 5.3%) Based upon our random samples, we are 99% confident that the proportion of elementary age students in Riverside who are fluent in English is greater than the proportion of elementary age students in Palm Springs who are fluent in English by at least 0.7% to as much as 5.3%

10.27 The state of California is working very hard to ensure that all elementary age students whose native language is not English become proficient in English by the sixth grade. Their progress is monitored each year using the California English Language Development test. The results for two school districts in southern California for the 2003 school year are given in the accom- panying table. Do the data indicate a significant difference in the 2003 proportions of students who are fluent in English for the two districts? Use α = .01. District Riverside Palm Springs long Number of students tested Percentage fluent 6124 5512 40 to aid 37 10 ibu2 ES.OF Answer: PR Pp: The proportion of elementary age students in Riverside who are fluent in English The proportion of elementary age students in Palm Springs who are fluent in English Hypotheses: HA: (PR - PP) 0 vs. Ho: (PR-PP) = 0 α = 1% • is (PR-PP) • 00=0 • is (PR - PP) (0.4 0.37) 0.03 = NR = 6124, np = 5512 PRX (1-PR) • σ is Ppx (1-Pp) + PRX (1-PR) Ppx (1-pp) + nR np nR np = 0.009 Rejection region: Reject Ho: (PR-Pp) = 0 if and only if the R.S.'s (PR-Pp) value is less than -Z0.5% PRX (1-PR) + nR Bpx (1-p) Пр =-(2.58) (0.009) = -0.023 ог ⚫ greater than +0.023 Test Statistic Value: (PR - PP) Test Decision: (0.4-0.37) = 0.03 Reject the null hypothesis since the test statistic falls into the RR Px(1-P)+P(1-Pp) (PR-PP)-Z0.5% ng np 99% C.I. for (PR-PP): (PR-PP) € (PR-PP) + Z0.5% PRX (1-PR)+ Ppx (1-Pp) nR np Interpretation: (PR-PP) € ((0.03 -0.023, 0.03+0.023) = (0.7%, 5.3%) Based upon our random samples, we are 99% confident that the proportion of elementary age students in Riverside who are fluent in English is greater than the proportion of elementary age students in Palm Springs who are fluent in English by at least 0.7% to as much as 5.3%

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
Section: Chapter Questions
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10.27 The state of California is working very hard to ensure that all elementary age students whose native language is not English become proficient in English by the sixth grade. Their progress is monitored each year using the California English Language Development test. The results for two school districts in southern California for the 2003 school year are given in the accom- panying table. Do the data indicate a significant difference in the 2003 proportions of students who are fluent in English for the two districts? Use α = .01. District Riverside Palm Springs long Number of students tested Percentage fluent 6124 5512 40 to aid 37 10 ibu2 ES.OF
Transcribed Image Text:10.27 The state of California is working very hard to ensure that all elementary age students whose native language is not English become proficient in English by the sixth grade. Their progress is monitored each year using the California English Language Development test. The results for two school districts in southern California for the 2003 school year are given in the accom- panying table. Do the data indicate a significant difference in the 2003 proportions of students who are fluent in English for the two districts? Use α = .01. District Riverside Palm Springs long Number of students tested Percentage fluent 6124 5512 40 to aid 37 10 ibu2 ES.OF
Answer: PR Pp: The proportion of elementary age students in Riverside who are fluent in English The proportion of elementary age students in Palm Springs who are fluent in English Hypotheses: HA: (PR - PP) 0 vs. Ho: (PR-PP) = 0 α = 1% • is (PR-PP) • 00=0 • is (PR - PP) (0.4 0.37) 0.03 = NR = 6124, np = 5512 PRX (1-PR) • σ is Ppx (1-Pp) + PRX (1-PR) Ppx (1-pp) + nR np nR np = 0.009 Rejection region: Reject Ho: (PR-Pp) = 0 if and only if the R.S.'s (PR-Pp) value is less than -Z0.5% PRX (1-PR) + nR Bpx (1-p) Пр =-(2.58) (0.009) = -0.023 ог ⚫ greater than +0.023 Test Statistic Value: (PR - PP) Test Decision: (0.4-0.37) = 0.03 Reject the null hypothesis since the test statistic falls into the RR Px(1-P)+P(1-Pp) (PR-PP)-Z0.5% ng np 99% C.I. for (PR-PP): (PR-PP) € (PR-PP) + Z0.5% PRX (1-PR)+ Ppx (1-Pp) nR np Interpretation: (PR-PP) € ((0.03 -0.023, 0.03+0.023) = (0.7%, 5.3%) Based upon our random samples, we are 99% confident that the proportion of elementary age students in Riverside who are fluent in English is greater than the proportion of elementary age students in Palm Springs who are fluent in English by at least 0.7% to as much as 5.3%
Transcribed Image Text:Answer: PR Pp: The proportion of elementary age students in Riverside who are fluent in English The proportion of elementary age students in Palm Springs who are fluent in English Hypotheses: HA: (PR - PP) 0 vs. Ho: (PR-PP) = 0 α = 1% • is (PR-PP) • 00=0 • is (PR - PP) (0.4 0.37) 0.03 = NR = 6124, np = 5512 PRX (1-PR) • σ is Ppx (1-Pp) + PRX (1-PR) Ppx (1-pp) + nR np nR np = 0.009 Rejection region: Reject Ho: (PR-Pp) = 0 if and only if the R.S.'s (PR-Pp) value is less than -Z0.5% PRX (1-PR) + nR Bpx (1-p) Пр =-(2.58) (0.009) = -0.023 ог ⚫ greater than +0.023 Test Statistic Value: (PR - PP) Test Decision: (0.4-0.37) = 0.03 Reject the null hypothesis since the test statistic falls into the RR Px(1-P)+P(1-Pp) (PR-PP)-Z0.5% ng np 99% C.I. for (PR-PP): (PR-PP) € (PR-PP) + Z0.5% PRX (1-PR)+ Ppx (1-Pp) nR np Interpretation: (PR-PP) € ((0.03 -0.023, 0.03+0.023) = (0.7%, 5.3%) Based upon our random samples, we are 99% confident that the proportion of elementary age students in Riverside who are fluent in English is greater than the proportion of elementary age students in Palm Springs who are fluent in English by at least 0.7% to as much as 5.3%
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