22 Heres a new idea for treating advanced melanoma the most

22. Here\'s a new idea for treating advanced melanoma, the most serious kind of skin cancer: genetically engineer white blood cells to better recognize and destroy cancer cells, then infuse these cells into patients. The subjects in a small initial study were 11 patients whose melanoma had not responded to existing treatments. One outcome of this experiment is measured by a test for the presence of cells that trigger an immune response in the body and so may help fight cancer. Here are data for the 11 subjects: counts of active cells per 100,000 cells before and after infusion of the modified cells. The difference (after minus before) is the response variable.

Solution

s_d = sqrt [ ((d_i - d-bar)² / (n - 1) ]..here, d-bar = 156.2727

where d_i is the difference for pair i, d-bar is the sample mean of the differences, and n is the number of paired values.
so, sd = 234.5682...

standard error = 234.5682 / sqrt( 11) = 70.72496...

test statistic = (d-bar - 0) / Std.error = 2.209584...

p-value = 0.02579851 with df = 11-1 =10..
which will be accepted when alpha =0.01...