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A study was performed on melanoma patients who had not responded to existing treatments to see...

A study was performed on melanoma patients who had not responded to existing treatments to see if a new genetic engineering technique could help fight cancer. The outcome of this treatment is measured by the number of active cells that can trigger an immune response in the body. The number of active cells per 100,000 cells was recorded before and after treatment for each patient in the following table.
Before 14 0 1 0 0 15 0 2 4 0 After 40 5 2 201 143 532 2 2 11 16
Can it be shown that this treatment significantly increases the true mean number of active cells? Assume that the distribution of differences is normal for your calculations.

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