There is evidence that cytotoxic T lymphocytes (T cells) participate in controll

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.

Do the data give evidence at the 1 % level that the mean count of T cells is higher after 20 days on blinatumomab?

The test statistic is t =____ (±0.001)

No or Yes?

Baseline 0.04 0.02 0 0.02 0.43 0.28 After 20 days 0.18 0.37 1.1 0.15 1.12 0.24 Difference 0.14 0.35 1.1 0.13 0.69 -0.04

Explanation / Answer

Data:     

n = n1 = n2 = 6    

d-bar = 0.395    

s (of d) = 0.4267    

Hypotheses:     

Ho: d-bar 0    

Ha: d-bar > 0    

Decision Rule:     

= 0.1    

Degrees of freedom = 6 - 1 = 5

Critical t- score = 1.475884037   

Reject Ho if t > 1.475884037    

Test Statistic:     

SE = s/n = 0.4267/6 = 0.174199546   

t = d-bar/SE = 0.395/0.17419954554093 = 2.268   

p- value = 0.036332283    

Decision (in terms of the hypotheses):    

Since 2.267514526 > 1.476 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

It appears that 1 > 2

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