Question

Comparison of peak expiratory flow rate (PEFR) before and after a walk on a cold winter's day for a random sample of 9 asthmatics. Use the following data to determine if the patients conditioned changed after a walk. Present your results and make some interpretations.

Subject	Before	After
1	312	300
2	242	201
3	340	232
4	388	312
5	296	220
6	254	256
7	391	328
8	402	330
9	290	231

Answer 1

See the data collected on the same subject so it is dependent data .

Also assume that the data comes from the normal population.

For dependent data set we use pair t test.

Here we want to test " if the patients conditioned changed after a walk"

Let's write null hypothesis (H₀) and altermative hypothesis(H₁)

Let's used excel :

Step 1) Enter the given data in excel columns.

Step 2) Click on Data >>>Data Analysis >>> t-Test: Pair Two sample for Means

then click on OK

In variable 1 Range select data of Before

In variable 1 Range select data of After

Hypothesized mean difference : 0

Select Labels

Then click on Output range and select any empty cell

See the following image

Then click on OK

So we get the following output

From the above output, we get

test statistic value = t = 4.926

p-value = 0.001

If level of significance is not given then take it as 0.05

Here p-value = 0.001 < level of significance = 0.05 so we reject the null hypothesis.

Conclusion:

At 5% level of significance there is sufficient evidence to say that the patients conditioned changed after a walk.