Question

You want to see if there is a relationship between how anxious someone is and their favourite colour. You assume that people who like colours like red or orange are more likely to be anxious than those who like colours like blue or green. From your population, 50 percent report liking red or orange and 50% report liking blue or green. You then give them an anxiety test.  Anxiety scores range from 0-25 (0 being the lowest, 25 being the highest level of anxiety). The results are in the table below. What is your conclusion?

	Warm	Cool	D	D2
	20	23	-3	9
	24	21	3	9
	14	20	-6	36
	15	17	-2	4
	18	23	-5	25
	17	25	-8	64
	20	23	-3	9
	13	25	-12	144
	21	21	0	0
ΣX	162	198	-36	300
ΣX²	3020	4408	300	27012
SS	104	52	156	17012

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 <   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   1                  
mean of sample 1,    x̅1=   18.000                  
standard deviation of sample 1,   s1 =    3.606                  
size of sample 1,    n1=   9                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   22.000                  
standard deviation of sample 2,   s2 =    2.550                  
size of sample 2,    n2=   9                  
                          
difference in sample means =    x̅1-x̅2 =    18.0000   -   22.0   =   -4.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    3.1225                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.4720                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -4.0000   -   0   ) /    1.47   =   -2.7175
                          
Degree of freedom, DF=   n1+n2-2 =    16                  
t-critical value , t* =        -1.746   (excel function: =t.inv(α,df)              
Decision:   | t-stat | > | critical value |, so, Reject Ho

                   
p-value =        0.007609   [ excel function: =T.DIST(t stat,df) ]               
Conclusion:     p-value <α , Reject null hypothesis