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In a Study of the Effectiveness of Physical Exercise in Weight

question 44

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In a study of the effectiveness of physical exercise in weight reduction, 12 subjects followed a program of physical exercise for two months. Their weights (in pounds) before and after this program are shown in the table. Use Wilcoxon's signed -ranks test and a significance level of
0) 05 to test the claim that the exercise program has no effect on weight.  Before 162190188152148127195164175156180136 After 157194179149135130183168168148170138\begin{array} { l l l l l l l l l l l l l } \text { Before } & 162 & 190 & 188 & 152 & 148 & 127 & 195 & 164 & 175 & 156 & 180 & 136 \\\hline \text { After } & 157 & 194 & 179 & 149 & 135 & 130 & 183 & 168 & 168 & 148 & 170 & 138\end{array}
What would be the signed rank for the column with values of 175 and 168 ?


Definitions:

Red Bone Marrow

The type of bone marrow that is involved in the production of red blood cells, white blood cells, and platelets.

Antigens

Substances or molecules that, when introduced into the body, trigger an immune response leading to the production of antibodies.

Cytokines

Small proteins important in cell signaling, with roles in the immune system, including mediating and regulating immunity, inflammation, and hematopoiesis.

Allergy

A condition in which the immune system reacts abnormally to a foreign substance.

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