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. Given are the T cell counts (10001000 per microliter) at baseline (beginning of the study) and after 2020 days on blinatumomab for six subjects in the study. The difference, after 2020 days minus baseline, is the response variable.

Baseline	0.040.04	0.020.02	0.000.00	0.020.02	0.380.38	0.330.33
After 20 days	0.280.28	0.470.47	1.301.30	0.250.25	1.221.22	0.440.44
Difference	0.240.24	0.450.45	1.301.30	0.230.23	0.840.84	0.110.11

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Do the data give evidence at the 5%5% level that the mean count of T cells is higher after 2020 days on blinatumomab? Answer each question to help determine this.

STATE: Will blinatumomab help cancer patients recruit T cells?

PLAN: Let ?μ represent the mean increase in T cell counts after 2020 days of blinatumomab. Select the correct hypotheses we will test.

?0:?=0 versus ??:?≠0H0:μ=0 versus Ha:μ≠0

?0:?=0 versus ??:<?H0:μ=0 versus Ha:<μ

?0:?=0 versus ??:?>0H0:μ=0 versus Ha:μ>0

?0:?≠0 versus ??:?=0H0:μ≠0 versus Ha:μ=0

?0:?=0 versus ??:?>20H0:μ=0 versus Ha:μ>20

SOLVE: Find ?¯x¯ , and ?t . (Enter your answer for ?¯x¯ rounded to four decimal places, and your answer for ?t rounded to three decimal places.)

?¯=x¯=

?=t=

Using software, find the ?‑P‑value. (Enter your answer rounded to four decimal places.)

?=P=

CONCLUDE: Does the data give evidence at the 5%5% level that the mean count of T cells is higher after 2020 days on blinatumomab?

no

yes

Answer 1

?0:?=0 versus ??:?>0  

xbar =0.5283

test statistic            =

(d̅-μd)/Se         =

2.830

p value =0.0183

Conclude: yes (since p value <0.05)