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 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.

469 | 503 |

534 | 533 |

666 | 526 |

538 | 410 |

534 | 531 |

588 | 594 |

497 | 464 |

608 | 485 |

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 *μ*_{1} = population
mean verbal score of students whose parents are college graduates
with a bachelor's degree and *μ*_{2} = population
mean verbal 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.

*H*_{0}: *μ*_{1} −
*μ*_{2} = 0

*H*_{a}: *μ*_{1} −
*μ*_{2} ≠ 0

*H*_{0}: *μ*_{1} −
*μ*_{2} ≥ 0

*H*_{a}: *μ*_{1} −
*μ*_{2} < 0

*H*_{0}: *μ*_{1} −
*μ*_{2} < 0

*H*_{a}: *μ*_{1} −
*μ*_{2} = 0

*H*_{0}: *μ*_{1} −
*μ*_{2} ≠ 0

*H*_{a}: *μ*_{1} −
*μ*_{2} = 0

*H*_{0}: *μ*_{1} −
*μ*_{2} = 0

*H*_{a}: *μ*_{1} −
*μ*_{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 *α* = 0.05, what is your conclusion?

Reject *H*_{0}. There is insufficient evidence to
conclude that higher population mean verbal scores are associated
with students whose parents are college graduates.

Do not Reject *H*_{0}. There is sufficient
evidence to conclude that higher population mean verbal scores are
associated with students whose parents are college
graduates.

Do not reject *H*_{0}. There is insufficient
evidence to conclude that higher population mean verbal scores are
associated with students whose parents are college graduates.

Reject *H*_{0}. There is sufficient evidence to
conclude that higher population mean verbal scores are associated
with students whose parents are college graduates.

Answer #1

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...

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...

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...

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...

The comparisons of Scholastic Aptitude Test (SAT) scores based
on the highest level of education attained by the test taker's
parents were provided. 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 (College Board website, January 8, 2012). SAT math
scores for independent samples of students follow. The first sample
shows the SAT math test scores for students whose parents...

Verbal SAT scores students at university were reported to have a
mean of 580. At about the same time, several hundred students in
statistics courses there were surveyed, and asked to report their
Math and Verbal SAT scores.
Using the 391 students with nonmissing data for variable Verbal,
test whether or not the sampled students' mean Verbal SAT score is
consistent with a population mean of 580, reporting the
P-value for a test of
H0 : μ = 580 vs....

The College Board reported the following mean scores for the
Math part of the Scholastic Aptitude Test (SAT) is 515. Assume that
the population standard deviation of the test is 100.
What is the probability that a random sample of 64 test takers
will provide a sample mean test score between 505 and 520 on the
Mathematics part of the test?

A certain test preparation course is designed to improve
students' SAT Math scores. The students who took the prep course
have a mean SAT Math score of 507 while the students who did not
take the prep course have a mean SAT Math score of 501. Assume that
the population standard deviation of the SAT Math scores for
students who took the prep course is 45.7 and for students who did
not take the prep course is 32.1 The SAT...

A certain test preparation course is designed to improve
students' SAT Math scores. The students who took the prep course
have a mean SAT Math score of 507 while the students who did not
take the prep course have a mean SAT Math score of 501. Assume that
the population standard deviation of the SAT Math scores for
students who took the prep course is 45.7 and for students who did
not take the prep course is 32.1 The SAT...

A random sample of 37 second graders who participated in sports
had manual dexterity scores with mean 32.29 and standard
deviation
4.14.
An independent sample of 37 second graders who did not
participate in sports had manual dexterity scores with mean 31.88
and standard deviation
4.86.
(a)
Test to see whether sufficient evidence exists to indicate that
second graders who participate in sports have a higher mean
dexterity score. Use
α = 0.05.
State the null and alternative hypotheses. (Us...

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