Question

  A health researcher is interested in comparing 3 methods of weight loss: low calorie diet, low fat diet and high exercise regimen. He selected 15 moderately overweight subjects and randomly assigned 5 to each weight-loss program. The following weight reductions (in lbs) were observed after a one-month period. Test the hypothesis that the extent of weight reduction does not differ by type of weight-loss program.                    
    Low Fat                          :  7      7      5       4       6                    
    Low Calorie                    :  7     8      8       9       5                    
    High Exercise Regimen  :  7     9      7      8        8                  ​

Answer 1

The weight loss in these three methods does not differ because the average weight loss is very similar in all 3.

How to calculate the average weight loss?

To calculate the average weight loss in these three situations, we must add all the values and divide the result by the number of values, for example:

• 7 + 7 + 5 + 4 + 6 = 29
• 7 + 8 + 8 + 9 + 5 = 37
• 7 + 9 + 7 + 8 + 8 = 39

• 39 ÷ 5 = 7.8
• 37 ÷ 5 = 7.4
• 29 ÷ 5 = 5.8

According to the above, it can be inferred that the hypothesis that the difference between one program and another is not significant enough to consider one plan more or less effective than another, because radically differences are not shown in each case.

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