Question

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 0.43 0.41 After 20 days 0 0.37 1.2 0 1.12 0.34 Difference -0.04 0.35 1.2 -0.02 0.69 -0.07 Do the data give evidence at the 4% level that the mean count of T cells is higher after 20 days on blinatumomab? The test statistic is t = (±0.001) Yes No.

Answer 1

H0: Null Hypothesis: ( the mean count of T cells is not higher after 20 days on blinatumomab )

HA: Alternative Hypothesis: ( the mean count of T cells is higher after 20 days on blinatumomab ) (Claim)

From d values, the following statistics are calculated:

n = 6

= 0.3517

sd = 0.5106

= 0.04

df = 6 - 1 = 5

From Table, critical value of t = 2.1910

Test Statistic is given by:

Since calculated value of t = 1.6872 is less than critical value of t = 2.1918, the difference is not significant. Fail to rejectnull hypothesis.

Conclusion:
The data do not support the claim that the mean count of T cells is higher after 20 days on blinatumomab .