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.
Student’s Parents
College Grads High School Grades
485 487 442 492
534 533 580 478
650 526 479 425
554 410 486 485
550 515 528 390
572 578 524 535
497 448
592 469
a. Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean verbal score on the SAT if their parents attained a higher level of education.
b. What is the point estimate of the difference between the means for the two populations?
c. Compute the p-value for the hypothesis test.
d. At αα= .05, what is your conclusion?

Answer 1

Answer:

Step-by-step explanation:

Hello!

Be:

X₁: SAT score of a student whose parents are college graduates with a bachelor's degree.

X₂: SAT score of a student whose parents are high school graduates but do not have a college degree.

The researcher's hypothesis is that the students whose parents attained a higher level of education would on average score higher SAT.

a)

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

b)

The parameter of interest is  μ₁ - μ₂ and its point estimate is:

X[bar]₁ - X[bar]₂= 525 - 487= 38

c)

Assuming the variables have a normal distribution and the population variances are unknown but equal:

$t_{H_0}= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } = \frac{38}{56.30*\sqrt{\frac{1}{16} +\frac{1}{12} } } = 1.77$

P-value: P(t₂₆≥1.77)= 0.0445

d)

The decision rule using the p-value approach is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

P-value: 0.0445 < α: 0.05 ⇒ The decision is to reject the null hypothesis.

So you can conclude that the average SAT score of the students whose parents are college graduates with a bachelor's degree is higher than the SAT scores of students whose parents are high school graduates but do not have a college degree.

I hope this helps!