Nineteen individuals with asthma were enrolled in a study investigating the resp

Question

Nineteen individuals with asthma were enrolled in a study investigating the respiratory effects if Sulphur dioxide. During the study, two measurements were obtained for each subject. The first is the increase in the soecific airway resistance (SAR)- a measure of bronchoconstriction- from the time when the individual is at rest until after he or she has been exercising for 5 minutes; the second is the increase in SAR for the same subject after he or she has undergone a similar exercise test conducted in an atmosphere of 0.25ppm sulphur dioxide.

Increase in SAR (CmH20 *sec)

0.72

a) At the Alpha =0.05 level of significance, test the null hypothesis that the median difference in increase in specific airway resistance for the two occassions is equal to 0. what do you conclude?

b) Do you feel that it would have been appropriate to use the paired t-test to evaluate these data? why or why not.

Subject Air SO2 1 0.82

0.72

2 0.86 1.05 3 1.86 1.40 4 1.64 2.30 5 12.57 13.49 6 1.56 0.62 7 1.28 2.41 8 1.08 2.32 9 4.29 8.19 10 1.37 6.33 11 14.68 19.88 12 3.64 8.87 13 3.89 9.25 14 0.58 6.59 15 9.50 2.17 16 0.93 9.93 17 0.49 13.44 18 31.04 16.25 19 1.66 19.89

Explanation / Answer

First, the R output is given below:

> tt <- read.csv("clipboard",header=T,sep=" ")
> tt
Subject Air SO2
1 1 0.82 0.72
2 2 0.86 1.05
3 3 1.86 1.40
4 4 1.64 2.30
5 5 12.57 13.49
6 6 1.56 0.62
7 7 1.28 2.41
8 8 1.08 2.32
9 9 4.29 8.19
10 10 1.37 6.33
11 11 14.68 19.88
12 12 3.64 8.87
13 13 3.89 9.25
14 14 0.58 6.59
15 15 9.50 2.17
16 16 0.93 9.93
17 17 0.49 13.44
18 18 31.04 16.25
19 19 1.66 19.89
> t.test(tt$Air,tt$SO2)

Welch Two Sample t-test

data: tt$Air and tt$SO2
t = -1.1854, df = 35.114, p-value = 0.2438
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-7.331957 1.925641
sample estimates:
mean of x mean of y
4.933684 7.636842

> t.test(tt$Air,tt$SO2,pair=TRUE)

Paired t-test

data: tt$Air and tt$SO2
t = -1.6862, df = 18, p-value = 0.109
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-6.0712424 0.6649266
sample estimates:
mean of the differences
-2.703158

a) As 0.05 level of significance, the null ypothesis that the media difference in increase in specific airway resistance for the two occassions is equal to 0 is not rejected.

(b) Paired t-test is more appropriate since the similar exercise is carried out on same subject for the soecific airway resistance , though the conclusion does not change.

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