Question

Eight artists have been asked to rate the visual characteristics of a painting done first by black and white, and then in multicolor.. After each of the paintings is finished, it is rated on a scale from 1 to 5 with 1 being best and 5 being worst. The results of the rating were shown below: Can you conclude that multicolor painting is better than just black and white? (Use α = 0.05.)

ARTTIST	BLACK AND WHITE	MULTICOLOR
A	5	1
B	4	2
C	1	2
D	4	3
E	3	1
F	4	4
G	4	5
H	2	3

Answer 1

µd = µ _{black and white} - µ_multicolor

Ho :   µd=   0
Ha :   µd <   0

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Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
5	1	4.000	10.5625
4	2	2.000	1.5625
1	2	-1.000	3.0625
4	3	1.000	0.0625
3	1	2.000	1.5625
4	4	0.000	0.5625
4	5	-1.000	3.0625
2	3	-1.000	3.0625

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	27	21	6	23.5

mean of difference ,    D̅ =ΣDi / n =   0.7500
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    1.8323

std error , SE = Sd / √n =    1.8323   / √   8   =   0.6478      
                          
t-statistic = (D̅ - µd)/SE = (   0.75   -   0   ) /    0.6478   =   1.158

                          
Degree of freedom, DF=   n - 1 =    7                  

p-value =        0.8575 [excel function: =t.dist(t-stat,df) ]              
Conclusion:     p-value>α , Do not reject null hypothesis          

there is no enough evidence to conclude that multicolor painting is better than just black and white