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:
<u>Part a:</u>
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.
<u>Part b:</u>
The point estimate of the difference between the means for the two populations is the difference of sample means
<u>x1`- x2`</u>
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
<u>592 469 350,464 219,961 </u>
<u>∑xi = 8400 ∑xi ²= 4,462,962 </u>
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
<u>524 535 274,576 286,225 </u>
<u>∑xi = 5844 ∑xi ²= 2,875,484 </u>
x2`= ∑ xi/n2= 5844/12= 487
Using statistic calculator Using formula : σ(n-1)
s2= 51.7476
x1`- x2`= 525- 487= 38
<u>The test statistic is </u>
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:
<u>Part C. </u>
The p-value is 0.041647.
The result is less than 0.05.
<u>Result:</u>
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.