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 485 487 550 533 650 526 538 410 550 531 556 578 481 432 608 485 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 μ1 = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ2 = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) a. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 b. H0: μ1 − μ2 ≠ 0 Ha: μ1 − μ2 = 0 c. H0: μ1 − μ2 ≥ 0 Ha: μ1 − μ2 < 0 d. H0: μ1 − μ2 ≤ 0 Ha: μ1 − μ2 > 0 e. H0: μ1 − μ2 < 0 Ha: μ1 − μ2 = 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? 1. Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. 2. 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. 3. 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. 4. Reject H0. There is insufficient evidence to conclude that higher population mean verbal scores are associated with 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 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 485 487 550 533 650 526 538 410 550 531 556 578 481 432 608 485 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 μ1 = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ2 = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) a. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 b. H0: μ1 − μ2 ≠ 0 Ha: μ1 − μ2 = 0 c. H0: μ1 − μ2 ≥ 0 Ha: μ1 − μ2 < 0 d. H0: μ1 − μ2 ≤ 0 Ha: μ1 − μ2 > 0 e. H0: μ1 − μ2 < 0 Ha: μ1 − μ2 = 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? 1. Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. 2. 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. 3. 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. 4. Reject H0. 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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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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College Grads

485	487
550	533
650	526
538	410
550	531
556	578
481	432
608	485

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 μ₁ = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ₂ = population mean verbal score of students whose parents are high school graduates but do not have a college degree.)

a. H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

b. H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

c. H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

d. H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

e. H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 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?

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

2. 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.

3. 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.

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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