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 Grads485503534517634526554394566531572594481448592469High School Grads442492580478479425486485528390524535(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 ?1 = population mean verbal score of students whose parents are college graduates with a bachelor's degree and ?2 = population mean verbal score of students whose parents are high school graduates but do not have a college degree.)A) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0B) H0: ?1 − ?2 ≠ 0Ha: ?1 − ?2 = 0 C)H0: ?1 − ?2 ≤ 0Ha: ?1 − ?2 > 0D) H0: ?1 − ?2 < 0Ha: ?1 − ?2 = 0E) H0: ?1 − ?2 ≥ 0Ha: ?1 − ?2 < 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? = 0.05,what is your conclusion?A)Do not reject H0. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.B) Reject H0. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. C) Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.D) Do not Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

We are given two independent samples here 1) SAT math test scores for students whose parents are…

Answered: The College Board provided comparisons…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 3E

See similar textbooks

Related questions

Question

100%

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

485	503
534	517
634	526
554	394
566	531
572	594
481	448
592	469

High School Grads

442	492
580	478
479	425
486	485
528	390
524	535

(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 ?₁ = population mean verbal score of students whose parents are college graduates with a bachelor's degree and ?₂ = population mean verbal score of students whose parents are high school graduates but do not have a college degree.)

A) H₀: ?₁ − ?₂ = 0

H_a: ?₁ − ?₂ ≠ 0

B) H₀: ?₁ − ?₂ ≠ 0

H_a: ?₁ − ?₂ = 0

C)H₀: ?₁ − ?₂ ≤ 0

H_a: ?₁ − ?₂ > 0

D) H₀: ?₁ − ?₂ < 0

H_a: ?₁ − ?₂ = 0

E) H₀: ?₁ − ?₂ ≥ 0

H_a: ?₁ − ?₂ < 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)

? = 0.05,

what is your conclusion?

A)Do not reject H₀. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

B) Reject H₀. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

C) Reject H₀. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

D) Do not Reject H₀. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here