Question

In determining the relationship of a professor’s exams, a department checked students’

performances on the midterm and final exams in a class. Based on the following data, what can you say

about the relationship of the exam scores? ( )

H0:

H1:

=

Decision Rule:

Student Midterm Final

A 63 110

B 63 118

C 63 103

D 66 120

E 68 125

F 64 125

G 64 120

H 69 120

Test:

Conclusion:

2b) Based on your results above, what Final Exam score would you predict for a student whose

Midterm Exam score was 71?

Answer 1

Ho:   ß1=   0
H1:   ß1╪   0

------------

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
63	110	4.0000	58.1406	15.250
63	118	4.0000	0.1406	-0.750
63	103	4.0000	213.8906	29.250
66	120	1.0000	5.6406	2.375
68	125	9.0000	54.3906	22.125
64	125	1.0000	54.3906	-7.375
64	120	1.0000	5.6406	-2.375
69	120	16.0000	5.6406	9.500

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	520.00	941.00	40.00	397.88	68.00
mean	65.00	117.63	SSxx	SSyy	SSxy

sample size ,   n =   8          
here, x̅ = Σx / n=   65.000   ,     ȳ = Σy/n =   117.625  
               1.809615385  
SSxx =    Σ(x-x̅)² =    40.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   68.0          
                  
estimated slope , ß1 = SSxy/SSxx =   68.0   /   40.000   =   1.70000

estimated std error of slope =Se(ß1) = Se/√Sxx =    6.859   /√   40.00   =   1.0845
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    1.7000   /   1.0845   =   1.5675
                  
t-critical value=    2.4469   [excel function: =T.INV.2T(α,df) ]          
Degree of freedom ,df = n-2=   6              
p-value =    0.1680              
decison :    p-value>α , do not reject Ho              
Conclusion:   do not Reject Ho , so there is no enough evidence of significant relationship

b)

precdicted final score=    ȳ = 117.625  

(please try 127.83 if above gets wrong)