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 onaverage 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. Thesecond sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.College GradsHigh School Grads501471442492534533580478634526479425554426486485534515528390556594524535481464592453(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 mathscore 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 populationvariances are unequal when conducting the t-test.O Ho: H1 - Hz 0Hoi Hy- Hz #0Hai 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 mathscore 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 populationvariances are unequal when conducting the t-test.Ho: Hy - H2 0Ho: H1 - H2 #0H: 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.

Name: The College Board provided comparisons of Scholastic Aptitude Test (S
Uploaded: 2024-03-20T07:07:12.000Z
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Description: 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 educat

Question

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 onaverage 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. Thesecond sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.College GradsHigh School Grads501471442492534533580478634526479425554426486485534515528390556594524535481464592453(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 mathscore 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 populationvariances are unequal when conducting the t-test.O Ho: H1 - Hz < 0Hai H1- Hz = 0O Ho: H1 - H2 2 oO Ho: H1 - H2 = 0Hai Hy - Hz#0O Ho: H1 - H2 = 0Hai H1- Hz>0Hoi Hy- Hz #0Hai 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 mathscore 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 populationvariances are unequal when conducting the t-test.Ho: Hy - H2 < 0Ha: H1 - H2 = 0O Ho: H1 - H2 2 0O Ho: H1 - H2 = 0Hai Hy - Hz # 0Ho: H - H2 = 0Hai Hy - Hz> 0Ho: H1 - H2 #0H: 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.

Accepted Answer

Solution:
Let x=  College grades   and   y =  Highschool grades.
n1=16  Sample size of college…