220 1,171 1,123 245 Sums It seems that almost 50 pounds were lost in aggregate b
ID: 3056490 • Letter: 2
Question
220 1,171 1,123 245 Sums It seems that almost 50 pounds were lost in aggregate by these eight people and that the program actually does something. But you, as the statistician, are not convinced. So you use these data to test at 99% confidence and the dependent sample approach, that there is indeed a significant weight loss a) State the Null and Alternative hypotheses (1) b) Construct the PDF and state the Rejection Rule (1, 1) c) Perform the test i. What is the value of d ? (2) ii. What is the value of Sd? (2) ii What is the value of ttest ? (2) d) What is your decision? (1) e) What do you tell your friends? (1) (Remember precision and units.)Explanation / Answer
Following is the calculation table;
Person ID
Before (X)
After (Y)
d = X - Y
d2
1
125
120
-5
25
2
98
96
-2
4
3
123
127
4
16
4
112
115
3
9
5
187
161
-26
676
6
154
168
14
196
7
127
116
-11
121
8
245
220
-25
625
Total
-48
1672
H0 : Joining the ‘Calorie Counter’ group does not have any effect on weight (d = 0)
Vs
H1: Joining the ‘Calorie Counter’ group does reduces weight (d < 0)
Thus on an average there is loss of 6 pound weight.
Therefore sd = 14.06109
T test = 8 *(-6)/14.06109 = 1.206916
T critical at 5% LOS with 7 degrees of freedom = 2.3646
As T test < T critical it implies that H0 is accepted. Hence there is NO effect on weight loss after joining the ‘Calorie Counter’ group.
Person ID
Before (X)
After (Y)
d = X - Y
d2
1
125
120
-5
25
2
98
96
-2
4
3
123
127
4
16
4
112
115
3
9
5
187
161
-26
676
6
154
168
14
196
7
127
116
-11
121
8
245
220
-25
625
Total
-48
1672
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