Question

CORRELATION

1. A researcher is interested in how self-efficacy in statistics (how well you feel you can do statistics) is related to life enjoyment. He has his participants take a self-efficacy questionnaire and then a life enjoyment questionnaire. Both measures are on an 11-point scale. The data is as follows:

participant	stats self-efficacy	life enjoyment
A	10	11
B	9	10
C	10	11
D	11	11
E	2	3
F	10	10
G	11	10
H	10	9
I	9	8
J	10	11

b. What are the null and research hypotheses?
c. What is the mean of X?
What is the mean of Y?
Find the deviances for both groups. (X – My) and (Y – My)
Multiply the deviances like in the lecture
Sum these.
What number do you get? ___________________________
This is the numerator
Square the deviances in X and Y
What is the Sum of Squares of X?
What is the Sum of Squares of Y?
What do you get when you multiply SSx and SSy? _______________________________
Take the square root of that ____________________________
This is your denominator
d. What is r? ______________________
e. What is the critical value? ___________________________________
f. What is your decision? ______________________________

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
10	11	0.64	2.56	1.28
9	10	0.04	0.36	-0.12
10	11	0.64	2.56	1.28
11	11	3.24	2.56	2.88
2	3	51.84	40.96	46.08
10	10	0.64	0.36	0.48
11	10	3.24	0.36	1.08
10	9	0.64	0.16	-0.32
9	8	0.04	1.96	0.28
10	11	0.64	2.56	1.28

sample size ,   n =   10      
here, x̅ = Σx / n=   9.20   ,     ȳ = Σy/n =   9.40
              

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	92	94	61.6	54.4	54.20
mean	9.20	9.40	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.9363
..........

correlation hypothesis test      
Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   10  
alpha,α =    0.05  
correlation , r=   0.9363  
t-test statistic = r*√(n-2)/√(1-r²) =        7.540
DF=n-2 =   8

  
critical t-value =    2.3060  

Decison:  test stat > critical value, So, Reject Ho  

.................

THANKS

revert back for doubt

please upvote