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School administrators selected a simple random sample of 50 elementary school students and divided them into 25 pairs, with members of each pair having equal indicators of academic ability in mathematics. School administrators then selected one student from each pair at random to participate in an alternative mathematics curriculum while the other student received a traditional curriculum. At the end of the year, all of the students received a mathematics skills assessment, measured on a 100- point scale. School administrators are interested in determining if the alternative curriculum helps or hinders student performance. They specify a null hypothesis corresponding to no difference between the two curriculums and an alternative hypothesis to indicate that the curriculums are different in some way, where is the mean difference in pairs of student's scores. Ho: μ = 0 Ha:μ ‡ 0 t = Group 1 2 Difference Description Alternative Traditional Alternative - Traditional Sample mean x₁ = 88.04 x2 = 75.16 x = 12.88 Sample standard deviation $1 = 8.556 $2 = 14.966 s = 19.223 Assume that the distribution of the mean differences is approximately normal. Find the t test statistic for testing the hypotheses about differences in student achievement. Standard error estimate SE₁ = 1.711 SE2 = 2.993 SE= 3.845 Give your answer precise to two decimal places.

School administrators selected a simple random sample of 50 elementary school students and divided them into 25 pairs, with members of each pair having equal indicators of academic ability in mathematics. School administrators then selected one student from each pair at random to participate in an alternative mathematics curriculum while the other student received a traditional curriculum. At the end of the year, all of the students received a mathematics skills assessment, measured on a 100- point scale. School administrators are interested in determining if the alternative curriculum helps or hinders student performance. They specify a null hypothesis corresponding to no difference between the two curriculums and an alternative hypothesis to indicate that the curriculums are different in some way, where is the mean difference in pairs of student's scores. Ho: μ = 0 Ha:μ ‡ 0 t = Group 1 2 Difference Description Alternative Traditional Alternative - Traditional Sample mean x₁ = 88.04 x2 = 75.16 x = 12.88 Sample standard deviation $1 = 8.556 $2 = 14.966 s = 19.223 Assume that the distribution of the mean differences is approximately normal. Find the t test statistic for testing the hypotheses about differences in student achievement. Standard error estimate SE₁ = 1.711 SE2 = 2.993 SE= 3.845 Give your answer precise to two decimal places.

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
Problem 8CR
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School administrators selected a simple random sample of 50 elementary school students and divided them into 25 pairs, with members of each pair having equal indicators of academic ability in mathematics. School administrators then selected one student from each pair at random to participate in an alternative mathematics curriculum while the other student received a traditional curriculum. At the end of the year, all of the students received a mathematics skills assessment, measured on a 100- point scale. School administrators are interested in determining if the alternative curriculum helps or hinders student performance. They specify a null hypothesis corresponding to no difference between the two curriculums and an alternative hypothesis to indicate that the curriculums are different in some way, where μ is the mean difference in pairs of student's scores. Ho: M = : 0 Ha: M0 t = Group 1 2 Difference Description Alternative Traditional Alternative Traditional Sample mean x₁ = 88.04 x2 75.16 x = 12.88 Sample standard deviation $1 = 8.556 S2 = 14.966 S = 19.223 Assume that the distribution of the mean differences is approximately normal. Find the t test statistic for testing the hypotheses about differences in student achievement. Standard error estimate SE₁ = 1.711 = 2.993 SE₂ SE = 3.845 Give your answer precise to two decimal places.
Transcribed Image Text:School administrators selected a simple random sample of 50 elementary school students and divided them into 25 pairs, with members of each pair having equal indicators of academic ability in mathematics. School administrators then selected one student from each pair at random to participate in an alternative mathematics curriculum while the other student received a traditional curriculum. At the end of the year, all of the students received a mathematics skills assessment, measured on a 100- point scale. School administrators are interested in determining if the alternative curriculum helps or hinders student performance. They specify a null hypothesis corresponding to no difference between the two curriculums and an alternative hypothesis to indicate that the curriculums are different in some way, where μ is the mean difference in pairs of student's scores. Ho: M = : 0 Ha: M0 t = Group 1 2 Difference Description Alternative Traditional Alternative Traditional Sample mean x₁ = 88.04 x2 75.16 x = 12.88 Sample standard deviation $1 = 8.556 S2 = 14.966 S = 19.223 Assume that the distribution of the mean differences is approximately normal. Find the t test statistic for testing the hypotheses about differences in student achievement. Standard error estimate SE₁ = 1.711 = 2.993 SE₂ SE = 3.845 Give your answer precise to two decimal places.
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