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	0.45	0.37
After 20 days	0.08	0.27	1.2	0.15	1.12	0
Difference	0.04	0.25	1.2	0.13	0.67	-0.37

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)

No

Yes

Answer 1

: mean difference in count of T cells between after 20 days on blinatumomab and baseline (beginning of the study)

(difference : after 20 days on blinatumomab - baseline (beginning of the study))

To Test whether there is evidence that the mean count of T cells is higher after 20 days on blinatumomab.

Null hypothesis :H_o :

Alternate Hypothesis : H_a : (Right Tailed test)

Sample data :

d: T cell counts (1000 per microliter) at baseline (beginning of the study) and after 20 days on blinatumomab for 6 subjects in the study and their difference (after 20 days on blinatumomab - baseline (beginning of the study))

n : sample size =6

Sample mean :

Baseline	After 20 days	d: Difference	d-	(d-)2
0.04	0.08	0.04	-0.28	0.0784
0.02	0.27	0.25	-0.07	0.0049
0	1.2	1.2	0.88	0.7744
0.02	0.15	0.13	-0.19	0.0361
0.45	1.12	0.67	0.35	0.1225
0.37	0	-0.37	-0.69	0.4761
	Total	1.92		1.4924
	Mean : = 1.92/6	0.32

Sample Size : n	6
Level of significance :	0.04
Degrees of Freedom : n-1	5

The test statistic is t = 1.4348;

For right tailed test

As P-Value i.e. is greater than Level of significance i.e (P-value:0.1054 > 0.04:Level of significance); Fail to Reject Null Hypothesis

The data does not give enough at 4% level of significance that the mean count of T cells is higher after 20 days on blinatumomab

Do the data give evidence at the 4 % level that the mean count of T cells is higher after 20 days on blinatumomab?

Ans : No