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The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. College Grads High School Grads 469 487 492 442 534 517 580 478 650 510 479 425 554 426 486 485 566 531 528 390 588 578 524 535 481 448 592 485 (a) Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let u, = population mean verbal score of students whose parents are college graduates with a bachelor's degree and u, = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) O Ho: H - H2 = 0 H: Hy- Hz #0 O Ho: H1 - H2 < 0 Hgi Hy - Hz = 0 O Ho: H2 - Hz # 0 H: Hy - Hz = 0 Ho: H – H2 5 0 Hai Hy- Hz > 0 Hoi Hy- Hz Z O Hi Hy - Hz

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. College Grads High School Grads 469 487 492 442 534 517 580 478 650 510 479 425 554 426 486 485 566 531 528 390 588 578 524 535 481 448 592 485 (a) Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let u, = population mean verbal score of students whose parents are college graduates with a bachelor's degree and u, = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) O Ho: H - H2 = 0 H: Hy- Hz #0 O Ho: H1 - H2 < 0 Hgi Hy - Hz = 0 O Ho: H2 - Hz # 0 H: Hy - Hz = 0 Ho: H – H2 5 0 Hai Hy- Hz > 0 Hoi Hy- Hz Z O Hi Hy - Hz

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. College Grads High School Grads 469 487 442 492 534 517 580 478 650 510 479 425 554 426 486 485 566 531 528 390 588 578 524 535 481 448 592 485 (a) Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let u, = population mean verbal score of students whose parents are college graduates with a bachelor's degree and u, = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) O Ho: H1 - H2 = 0 Hai M1 - H2 # 0 0 > Zri – Ti :0H Hai H1 - H2 = 0 Hoi Hy- Hz#0 Ha: H1 - H2 = 0 Hoi H1 - H2 s0 Ha: M1 - M2 > 0 Ho: Hy - Hz z O Ha: M1 - H2 < 0
Transcribed Image Text:The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. College Grads High School Grads 469 487 442 492 534 517 580 478 650 510 479 425 554 426 486 485 566 531 528 390 588 578 524 535 481 448 592 485 (a) Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let u, = population mean verbal score of students whose parents are college graduates with a bachelor's degree and u, = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) O Ho: H1 - H2 = 0 Hai M1 - H2 # 0 0 > Zri – Ti :0H Hai H1 - H2 = 0 Hoi Hy- Hz#0 Ha: H1 - H2 = 0 Hoi H1 - H2 s0 Ha: M1 - M2 > 0 Ho: Hy - Hz z O Ha: M1 - H2 < 0
(b) What is the point estimate of the difference between the means for the two populations? (c) Find the value of the test statistic. (Round your answer to three decimal places.) Compute the p-value for the hypothesis test. (Round your answer to four decimal places.) p-value = (d) At a = 0.05, what is your conclusion? O Reject Ho. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. O Do not Reject Ho. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. O Do not reject Ho. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. O Reject Ho. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.
Transcribed Image Text:(b) What is the point estimate of the difference between the means for the two populations? (c) Find the value of the test statistic. (Round your answer to three decimal places.) Compute the p-value for the hypothesis test. (Round your answer to four decimal places.) p-value = (d) At a = 0.05, what is your conclusion? O Reject Ho. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. O Do not Reject Ho. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. O Do not reject Ho. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. O Reject Ho. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.
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