Question

A company is research a new drug for cancer treatment. The drug is designed to reduce the size of a tumor. You are asked to test its effectiveness. You proceed to take samples from patients that are trying the drug. For each patient you take two measurements of its tumor, before and after the treatment. You want to see if the tumor's size has decreased. Assume the population distribution is normal and α = 0.05. The results of the samples (in millimeters, before and after treatment) are as follows:

Patient	Before	After
1	158	284
2	189	214
3	202	101
4	353	227
5	416	290
6	426	176
7	441	290

Answer 1

Given that,
null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.447
since our test is two-tailed
reject Ho, if to < -2.447 OR if to > 2.447
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 86.143
We have d = 86.143
pooled variance = calculate value of Sd= √S^2 = sqrt [ 143755-(603^2/7 ] / 6 = 123.7
to = d/ (S/√n) = 1.842
critical Value
the value of |t α| with n-1 = 6 d.f is 2.447
we got |t o| = 1.842 & |t α| =2.447
make Decision
hence Value of |to | < | t α | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 1.8425 ) = 0.115
hence value of p0.05 < 0.115,here we do not reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: 1.842
critical value: reject Ho, if to < -2.447 OR if to > 2.447
decision: Do not Reject Ho
p-value: 0.115
we do not have enough evidence to support the claim that For each patient you take two measurements of its tumor, before and after the treatment.
You want to see if the tumor's size has decreased.