Question

Long-distance runners have contended that moderate exposure to ozone increases lung capacity. To investigate this possibility, a researcher exposed 12 rats to ozone at the rate of 2 parts per million for a period of 30 days. The lung capacity of the rats was determined at the beginning of the study and again after the 30 days of ozone exposure. The lung capacities (in mL) are given here. Before Exposure 8.7 7.9 8.3 8.4 9.2 9.1 8.2 8.1 8.9 8.2 8.9 7.5 After Exposure 9.4 9.8 9.9 10.3 8.9 8.8 9.8 8.2 9.4 9.9 12.2 9.3 Is there sufficient evidence to support the conjecture that ozone exposure increases lung capacity? Use a .05. Report the p-value of your test. is this independent or paired data and why which nonparametric test would be appropriate to compare the two groups

Answer 1

A= [8.7,7.9,8.3,8.4,9.2,9.1,8.2,8.1,8.9,8.2,8.9,7.5]
B= [9.4,9.8,9.9,10.3,8.9,8.8,9.8,8.2,9.4,9.9,12.2,9.3]
A-B=[-0.7, -1.9, -1.6, -1.9, 0.3, 0.3, -1.6, -0.1, -0.5, -1.7, -3.3, -1.8]
Mean of A-B=-1.20833

Mean of the differences = -1.20833
The 95% CI for the mean difference is given by mean of diferences ± 1.65 ∗ t
=-1.208 ± 1.65 ∗ 2.200985

(-4.839959, 2.423292)
As zero is included in the CI, we can accept the null hypothesis. Thus, we can conclude that Ozone exposure increases lung capacity

Standard Deviation of the differences, ?? = 8.56
Standard Error = 1.013/sqrt(number of elements)=0.29

? = Mean of A-B /Standard Error of the mean = - 4.0577
From the t statistic table for p=0.025 an d degrees of freedom =11
t= 2.200985
For t=(-4.057763436135119 and degree of freedom =11 p=0.999485
i.e p value=1 approx.
It is a paired data as the sample is compared before and after an activity
Paired T test can be used to compare the tests.