College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test rage score higher on the SAT. The overall mean SAT math score was 514.1 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 ond sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. takers parents. A r esearch hypothesis was that students whose parents had attained a higher level of education would on College Grads High School Grads 501 471 442 492 534 533 580 478 634 526 479 425 554 426 486 485 534 515 528 390 556 594 524 535 481 464 592 453 OFormulate 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 math score of students whose parents are college graduates with a bachelor's degree and a, - population mean math score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test. O "o: H1 - H2 <0 O Mo: Hg - Hz z 0 O Ho: H1 - H2 = 0 O Ho: H - H2= o Hoi Hi - Hz > 0 O Ho: H: - H2 0

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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 514.1 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
501
471
442
492
534
533
580
478
634
526
479
425
554
426
486
485
534
515
528
390
556
594
524
535
481
464
592
453
(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 math
score of students whose parents are college graduates with a bachelor's degree and u, = population mean math score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population
variances are unequal when conducting the t-test.
O Ho: H1 - Hz < 0
Hai H1- Hz = 0
O Ho: H1 - H2 2 o
O Ho: H1 - H2 = 0
Hai Hy - Hz#0
O Ho: H1 - H2 = 0
Hai H1- Hz>0
Hoi Hy- Hz #0
Hai Hy - Hz = 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.)
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 514.1 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 501 471 442 492 534 533 580 478 634 526 479 425 554 426 486 485 534 515 528 390 556 594 524 535 481 464 592 453 (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 math score of students whose parents are college graduates with a bachelor's degree and u, = population mean math score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test. O Ho: H1 - Hz < 0 Hai H1- Hz = 0 O Ho: H1 - H2 2 o O Ho: H1 - H2 = 0 Hai Hy - Hz#0 O Ho: H1 - H2 = 0 Hai H1- Hz>0 Hoi Hy- Hz #0 Hai Hy - Hz = 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.)
(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 math
score of students whose parents are college graduates with a bachelor's degree and u, = population mean math score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population
variances are unequal when conducting the t-test.
Ho: Hy - H2 < 0
Ha: H1 - H2 = 0
O Ho: H1 - H2 2 0
O Ho: H1 - H2 = 0
Hai Hy - Hz # 0
Ho: H - H2 = 0
Hai Hy - Hz> 0
Ho: H1 - H2 #0
H: H1 - 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 Do not Reject Ho. There is sufficient evidence to conclude that higher population mean math 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 math scores are associated with students whose parents are college graduates.
O Reject Ho. There is sufficient evidence to conclude that higher population mean math scores are associated with students whose parents are college graduates.
O Reject Ho: There is insufficient evidence to conclude that higher population mean math scores are associated with students whose parents are college graduates.
Transcribed Image Text:(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 math score of students whose parents are college graduates with a bachelor's degree and u, = population mean math score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test. Ho: Hy - H2 < 0 Ha: H1 - H2 = 0 O Ho: H1 - H2 2 0 O Ho: H1 - H2 = 0 Hai Hy - Hz # 0 Ho: H - H2 = 0 Hai Hy - Hz> 0 Ho: H1 - H2 #0 H: H1 - 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 Do not Reject Ho. There is sufficient evidence to conclude that higher population mean math 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 math scores are associated with students whose parents are college graduates. O Reject Ho. There is sufficient evidence to conclude that higher population mean math scores are associated with students whose parents are college graduates. O Reject Ho: There is insufficient evidence to conclude that higher population mean math scores are associated with students whose parents are college graduates.
Expert Solution
Step 1

Solution:

Let x=  College grades   and   y =  Highschool grades.

n1=16  Sample size of college grades n2=12  Sample size of highschool gradesx=8368x=xn=836816=523  Sample mean  of college grades s12=(x-x)2n1-1= 3155.333  Sample variance of college grades.y=5844 y =yn2=584412=487   Sample mean  of highschool gradess22=(y-y)2n2-1=2677.818 Sample variance of highschool grades  

 

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