Question

The table below shows the weights of seven subjects before and after following a particular diet for two months. Subject / A / B / C / D / E / F / G ////////////////////////////////////////////////// Before / 165 / 151 / 196 / 175 / 179 / 172 / 191 ////////////////////////////////////////////////// After / 166 / 154 / 169 / 164 / 176 / 193 / 169 Using a 0.01 level of significance, test the claim that the diet is effective in reducing weight. Use the critical value method of hypothesis testing.

Answer 1

paired t test

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
165	166	-1	41.327
151	154	-3	71.041
196	169	27	465.327
175	164	11	31.041
179	176	3	5.898
172	193	-21	698.469
191	169	22	274.612

Ho :   µd=   0
Ha :   µd >   0
mean of difference ,    D̅ =ΣDi / n =   5.429                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    16.267                  
                          
std error , SE = Sd / √n =    16.2671   / √   7   =   6.1484      
                          
t-statistic = (D̅ - µd)/SE = (   5.428571429   -   0   ) /    6.1484   =   0.8829
                          
Degree of freedom, DF=   n - 1 =    6  

α=0.05   
t-critical value , t* =        1.9432   [excel function: =t.inv(α,df) ]               
                          
  
Decision: test stat < 1.9432 , Do not reject null hypothesis                     

there is no enough evidence to conclude that diet is effective in reducing weight

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