A crossove trail is a type of experiment used to compare two

A crossove trail is a type of experiment used to compare two drugs. Subject take one drug for a period of time, then switch to the other. The responses of the subjects are then compared using matched pair methods. In an experiment to compare two pain relivers, seven subjects took one pain reliver for two weeks, then switched to the other. They rated their pain level from 1 to 10, with large numbers representing higher levels of pain. The results were

Subject

1 2 3 4 5 6 7

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(DrugA) 6 3 4 5 7 1 4

(DrugB) 5 1 5 5 5 2 2

A. Find 98% confidence level for the difference of mean responses between the two drugs?

B. Can you conclude that the mean response differs between the two drugs?

i. State hypothesis.

ii. Compute P-value

iii. What is you conclusion?

Solution

A. Find 98% confidence level for the difference of mean responses between the two drugs?

Given a=1-0.98=0.02, t(0.01, df=6) =3.14 (from student t table)

So the lower bound is

mean difference - t*s/vn =0.714 -3.14*1.380/sqrt(7) =-0.9237957

So the upper bound is

mean difference +t*s/vn =0.714 +3.14*1.380/sqrt(7) =2.351796

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B. Can you conclude that the mean response differs between the two drugs?

i. State hypothesis.

Let mu_d be the mean difference between the two drugs.

Null hypohtesis: mu_d =0

Alternative hypothesis: mu_d not equal to 0

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ii. Compute P-value

The test statistic is

t=mean difference/(s/vn)

=0.714/(1.380/sqrt(7))

=1.37

It is a two-tailed test.

So the P-value= 2*P(t with df=6 >1.37) =0.2197 (from student t table)

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iii. What is you conclusion?

Since the p-value is larger than 0.02, we do not reject the null hypothesis.

So we can not conclude that the mean response differs between the two drugs