Question

1. You are testing H0:μ=100 against Ha:μ<100 with degrees of freedom of 24. The t statistic is -2.63 .

      The P-value for the statistic falls between      and        .

2. (20.31) The placebo effect is particularly strong in patients with Parkinson's disease. To understand the workings of the placebo effect, scientists measure activity at a key point in the brain when patients receive a placebo that they think is an active drug and also when no treatment is given. The same six patients are measured both with and without the placebo, at different times. The six differences (treatment minus control) had x⎯⎯⎯ = -0.358 and s = 0.179 .

The value of the t statistic (±0.01) is      

Is there significant evidence at the 5% level of a difference between treatment and control?.

YES OR NO ?

3. 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	0.28	0.4
After 20 days	0.18	0.27	1.1	0	1.12	0.24
Difference	0.14	0.25	1.1	-0.02	0.84	-0.16

Do the data give evidence at the 5 % level that the mean count of T cells is higher after 20 days on blinatumomab?    YES OR NO ?

The test statistic is t = ? (± 0.001)

Answer 1

1)

p value = 0.0075

0.005 < pvalue < 0.01

2)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (-0.358 - 0)/(0.179/sqrt(6))
t = -4.899

P-value Approach
P-value = 0.0045
As P-value < 0.05, reject the null hypothesis.

yes

3)

Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (0.36 - 0)/(0.5007/sqrt(6))
t = 1.761)