Question

In an investigation, you want to know if people in Group A and B has same height on average. (Total number of people 100)

A" (average height of group A)	165.0
B" (average height of group B)	185.0
D" (average of height differences of bwtween a person in A and a person in B)	-0.4
sA (sample standard deviation)	4.4
sB (sample standard deviation)	3.2
sD (sample standard deviation)	2.3

1 Write down hypotheses and test should conduct? Please define variables clearly.

2 Let Alpha = 0.1. Conduct a hypothesis test (p-values) based on the data above. Write down conclusion?

Answer 1

a)

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0          

2 sample indpendent t test

b)
                          
Level of Significance ,    α =    0.1                  
                          
Sample #1   ---->   A                
mean of sample 1,    x̅1=   165.00                  
standard deviation of sample 1,   s1 =    4.40                  
size of sample 1,    n1=   50                  
                          
Sample #2   ---->   B                  
mean of sample 2,    x̅2=   185.00                  
standard deviation of sample 2,   s2 =    3.20                  
size of sample 2,    n2=   50                  
                          
difference in sample means =    x̅1-x̅2 =    165.0000   -   185.0   =   -20.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    3.8471                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.7694                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -20.0000   -   0   ) /    0.77   =   -25.994
                          
Degree of freedom, DF=   n1+n2-2 =    98                  

p-value =        0.000000   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value <α , Reject null hypothesis                      
                          
There is enough evidence that  there is difference in Group A and B height.

THANKS

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