Question

Low-fat or low-carb? Are low-fat diets or low-carb diets more effective for
weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six
months. At the end of that time, the sample mean weight loss was 4.7 kilograms
with a sample standard deviation of 7.16 kilograms. A second sample of 79
subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kilograms
with a standard deviation of 5.90 kilograms. Can you conclude that the mean
weight loss differs between the two diets? Use α = 0.01.
a) State the hypotheses.
b) Compute the test statistic, t.
c) How many degrees of freedom are there (simple method)?
d) Do you reject H0? Give a concluding statement.

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.01                  
                          
Sample #1   ---->   successful                  
mean of sample 1,    x̅1=   4.70                  
standard deviation of sample 1,   s1 =    7.16                  
size of sample 1,    n1=   77                  
                          
Sample #2   ---->   unsuccessful                  
mean of sample 2,    x̅2=   2.60                  
standard deviation of sample 2,   s2 =    5.90                  
size of sample 2,    n2=   79                  
                          
difference in sample means =    x̅1-x̅2 =    4.7000   -   2.6   =   2.100  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    6.5522                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.0493                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   2.1000   -   0   ) /    1.05   =   2.001
                          
Degree of freedom, DF=   n1+n2-2 =    154                 
  
p-value =        0.047107   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value>α , Do not reject null hypothesis              

MEAN WEIGHT loss do not differ between two diets

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