16. The College Board provided comparisons of Scholastic Aptitude Test (SAT) sco

ID: 3364011 • Letter: 1

Question

16. 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 aver- age score higher on the SATThe overall mean SAT math score was 514 (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 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 Students' Parents College Grads 485 487 534 533 650 526 54 410 550 515 572 578 497 448 592 469 High School Grads 442 492 580 478 479 425 486 485 528 390 524 535 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 a. 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 = .05, what is your conclusion?

Explanation / Answer

Let

X = SAT math score of students whose parents are college graduates with a bachelor’s degree,

Y = SAT math score of students whose parents are high school graduates but do not have college degree.

We assume

X ~ N(µ1, 12) and Y ~ N(µ2, 22), where neither 1 nor 2 is known, but are assumed to be equal.

Part (a)

Claim: Students show a higher population mean math score on the SAT if their parents attained a higher level of education.

Hypotheses:

Null: H0: µ1 = µ2 Vs Alternative: HA: µ1 > µ2 ANSWER

Part (b)

Point estimate for the difference between the means for the two populations

= Xbar – Ybar where Xbar and Ybar are respectively the means of sample of SAT math scores of students with college graduate parents and high school graduate parents.

= 525 - 487

= 38 ANSWER

Part (c)

Test Statistic:

t = (Xbar - Ybar)/[s{(1/n1) + (1/n2)}] where

s2 = {(n1 – 1)s12 + (n2 – 1)s22}/(n1 + n2 – 2);

Xbar and Ybar are sample averages and s1, s2 are sample standard deviations based on n1 observations on X and n2 observations on Y respectively.

p-value = P(t n1 + n2 – 2 > tcal)

Calculations

Summary of Excel calculations is given below:

Xbar

525

Ybar

487

59.42054

51.74764

s1^2

3530.8

s2^2

2677.818

s^2

3169.923

56.30207

tcal =

1.767384

0.05

tcrit =

1.705618

p-value =

0.04445 ANSWER

Part (d)

To perform the full test,

Decision Criterion (Rejection Region):

Reject H0 if p-value <

Decision:

Taking = 0.05, H0 is rejected since p-value < .

Conclusion:

There is sufficient evidence to suggest that the claim is valid.

i.e., statistical evidence suggest that Students show a higher population mean math score on the SAT if their parents attained a higher level of education. ANSWER