Question

Hypothesis Testing (Two samples – means) Using the 5 step process:

After four weeks in the program, Weight Watchers wants to know if there is a difference between the weight loss in men as opposed to the weight loss in women. After four weeks, a sample of 40 men revealed a mean weight loss of 17.6 pounds while a sample of 55 women revealed a mean weight loss of 13.8 pounds. The standard deviation of weight loss in men and women is 5.8 pounds and 4.0 pounds respectively. At the 0.01 significance level, in the first four weeks, is there a difference between the weight loss in men as opposed to the weight loss in women?

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.01                  
                          
Sample #1   ---->   male   
mean of sample 1,    x̅1=   17.60                  
standard deviation of sample 1,   s1 =    5.80                  
size of sample 1,    n1=   40                  
                          
Sample #2   ---->  female   
mean of sample 2,    x̅2=   13.80                  
standard deviation of sample 2,   s2 =    4.00                  
size of sample 2,    n2=   55                  
                          
difference in sample means =    x̅1-x̅2 =    17.6000   -   13.8   =   3.80  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    4.8371                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.0052                 
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   3.8000   -   0   ) /    1.01   =   3.780
                          
Degree of freedom, DF=   n1+n2-2 =    93                  

p-value =        0.00028 (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value <α , Reject null hypothesis                      
                          
There is enough evidence to conclude that there a difference between the weight loss in men as opposed to the weight loss in women

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