Question

Each of eight influenza sufferers is given aspirin (on one day) and a buffered product (on another day) in order to alleviate symptoms accompanying influenza. The two treatments are given in a random order to each person. The length of time (in minutes) from taking the drug to the patient’s saying that he or she is improved is recorded. The following table contains the data:

1	2	3	4	5	6	7	8
17	15	12	18	17	14	16	17
10	15	13	14	15	10	14	16

Is there a difference in relief times between the buffered product and the aspirin? Use ?=0.05. Round any calculated sample statistics to two decimal places.

0.

1.

2.

3.

4.

5.

Answer 1

Before	after	difference	(d-dbar)^2
17 15 12 18 17 14 16 17	10 15 13 14 15 10 14 16	-7 0 1 -4 -2 -4 -2 -1 M: -2.38	21.39 5.64 11.39 2.64 0.14 2.64 0.14 1.89 S: 45.88

a) null and alternate hypothesis

H0:d=0

H1:d0

b) level of significance = 0.05

C) test statistics

Mean: -2.38
μ = 0
S² = SS⁄df = 45.88/(8-1) = 6.55
S²_M = S²/N = 6.55/8 = 0.82
S_M = √S²_M = √0.82 = 0.91

T-value Calculation

t = (M - μ)/S_M = (-2.38 - 0)/0.91 = -2.62

D) p value = 0.0342

E) since the p value is less than level of significance so we reject the null hypothesis.

So there sufficient evidence to conclude that there a difference in relief times between the buffered product and the aspirin.