Question

Find the parameters of interest, null and alternate hypothesis, statistic analysis, and conclusion of the context of the problem. Justify the conclusion.

Long-distance runners have said for decades that moderate exposure to ozone increases lung capacity. To investigate this possibility, an investigator measured lung capacity in a sample of 10 rats that he randomly selected. Lung capacity (in ml) was measured at the start of the study and 30 days after exposing the rats to ozone. The data set is shown below.

RATS: Before the Ozone exposition: After the Ozone exposition:

1 8.7 9.4

2 7.9 9.8

3 8.3 9.9

4 8.4 10.3

5 9.2 8.9

6 9.1 8.8

7 8.2 9.8

8 8.1 8.2

9 8.9 12.2

10 7.5 9.3

Answer 1

Solution:

The parameter of interest is lung capacity.

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: The moderate exposure to ozone does not increases lung capacity.

Alternative hypothesis: Ha: The moderate exposure to ozone increases lung capacity.

H0: µd = 0 versus Ha: µd > 0

This is a right tailed test.

We take difference as after minus before.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 1.23

Sd = 1.1557

n = 10

df = n – 1 = 9

α = 0.05

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (1.23 – 0)/[ 1.1557/sqrt(10)]

t = 3.3656

The p-value by using t-table is given as below:

P-value = 0.0042

P-value < α =0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the moderate exposure to ozone increases lung capacity.