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The comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents are 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 514. SAT math scores for independent samples of students follow. Two samples are contained in the Excel Online file below. 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
485
534
650
554
550
572
497
592
​Grads
487
533
526
410
515
578
448
469
​High School
442
580
479
486
528
524
​Grads
492
478
425
485
390
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. population mean math score parents college grads. population mean math score parents high school grads. _____ _____
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?

Respuesta :

akiran007

Answer:

H0 is rejected and Ha is accepted that the students show a higher population mean math score on the SAT if their parents attained a higher level of education.

Step-by-step explanation:

Part a:

The null and alternate hypothesis can be formulated as

H0 : u1 ≤ u2 the two means ( of students whose parents did or did not attain a higher level of education) are equal .

against the claim

Ha: u1 > u2 the students show a higher population mean math score on the SAT if their parents attained a higher level of education.

Part b:

The point estimate of the difference between the means for the two populations is the difference of sample means

x1`- x2`

525- 487= 38

Student’s Parents

College Grads

x                                            x²

485      487               235,225         237,169

534      533                  285,156        284,089

650     526                 422,500         267,676

554       410                   306,916          168,100

550      515                   302,500        265,225

572      578                      327,184        334,084

497      448                     247,009        200,704

592     469                  350,464         219,961          

∑xi = 8400                      ∑xi ²= 4,462,962          

x1`= ∑ xi/n1= 8400/16= 525

Using statistic calculator Using formula :  σ(n-1)

s1= 59.4205

High School Grads

x                                          x²

442          492                   195,364            242,064

580          478                    336,400            228,484

479           425                      229,441             180,625

486            485                     236,196            235,225

528            390                     278,784           152,100

524             535                     274,576           286,225        

∑xi = 5844                                 ∑xi ²= 2,875,484                

x2`= ∑ xi/n2= 5844/12= 487

Using statistic calculator Using formula :  σ(n-1)

s2= 51.7476

x1`- x2`= 525- 487= 38

The test statistic is

t= (x1`- x2`) / √ s1²/n1+ s2²/n2

t= 38/ √(59.4205)²/16 + (51.7476)²/12

t=38 / √3530.7958/16 + 2677.8141/12

t= 1.804

and the degrees of freedom is

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= [3530.7958/16 + (2677.8141/12) ]²/ (3530.7958/16)²/15 +(2677.8141/12)²/11

≈ 25

The degrees of freedom is always rounded in this calculation

From the table t∝ = 1.708

Hence critical value is t ≥ t∝

Reject H0:

Part C.

The p-value is 0.041647.

The result is less than  0.05.

Result:

H0 is rejected and Ha is accepted that the students show a higher population mean math score on the SAT if their parents attained a higher level of education.

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