Question

(20.48) There is evidence that cytotoxic T lymphocytes (T cells) participate in controlling tumor growth and that they can be harnessed to use the body's immune system to treat cancer. One study investigated the use of a T cell-engaging antibody, blinatumomab, to recruit T cells to control tumor growth. The data below are T cell counts (1000 per microliter) at baseline (beginning of the study) and after 20 days on blinatumomab for 6 subjects in the study. The difference (after 20 days minus baseline) is the response variable.

Baseline	0.04	0.02	0	0.02	0.47	0.37
After 20 days	0	0.37	1.1	0.15	1.12	0
Difference	-0.04	0.35	1.1	0.13	0.65	-0.37

Do the data give evidence at the 5% level that the mean count of T cells is higher after 20 days on blinatumomab?

The test statistic is t =  (±±0.001)

Answer 1

Null Hypothesis, Ho: There is no significant difference in the mean count of T cells after 20 days on blinatumomab i.e.   

Alternative Hypothesis, Ha: The mean count of T cells is higher after 20 days on blinatumomab i.e.

Test- Statistics: Under Ho,

here, and and n = 6

so , the value of test statistics is given as

p-value = P[ t > 1.425 ] = 0.106736

Decision: Since p-value > 0.05 so we fail to reject Ho at 5% level of significance

Conclusion: We have insufficient evidence to reject the claim that there is no significant difference in the mean count of T cells after 20 days on blinatumomab