Question

PEF (L/min)

SubjectChronic BronchitisHealthy Children

1 281 360

2 274 372

3 305 295

4 366 382

5 315 234

6 224 275

7 192 286

8 229 304

9 276 333

10 315 401

11 184 212

12 287 312

13 264 324

14 296 296

15 301 378

16 327 384

17 350 271

18 311 299

19 253 371

20 285 305

Based on data, is there evidence of a lower mean PEF in children with chronic bronchitis as compared to those without? Run the appropriate test in Excel and interpret the results.

Answer 1

Our objective here, is to test the claim whether there is an evidence of a lower mean PEF in children with chronic bronchitis as compared to those without based on the given data.

Let denote the mean PEF of children with and without chronic bronchitis respectively.We have to test:

Vs

Using excel:

Before running an independent sample t test, we need to verify whether our data satisfies all the assumptions of the test:

1. The dependent variable is continuous. (Here, the PEF measured in in children with and without chronic bronchitis) 2. The independent variable has two independent categories. (Here, "Chronic Bronchitis" has 2 independent categories 'With' and 'Without') 3. Independence of observations (We may assume that this independence is kept in mind while collecting data for the sample) 4. There are no significant outliers. To verify this assumption, we need to find out whether any of the observation falls below the range:

where Q₁ = 1st Quartile,  Q3 = 3rd Quartile, and IQR =Q3 -  Q₁

Substituting the values:

We find that two observations in Group 1 (PEF of children with chronic bronchitis) falls below the lower bound and hence, may be considered as outliers.)This is a violation of the assumption.

5. The data is normally distributed. 6. Homogeneity of variance: To test

Vs

Since, the p-value = 0.34 > 0.05, we fail to reject the null hypothesis, thereby concluding that the assumption of homogeneity of variance is satisfied.

Running an independent sample t test:

We find that the p-value 0.01 < 0.05, i.e. the probability of obtaining a result as extreme as the one obtained, when the null hypothesis is true is far lesser (than the fixed significance level 0.05, say). It implies that the chance of H₀ being true is very low. We may reject H₀ at 5% level of significance.

We may conclude that we have sufficient evidence to support the claim that mean PEF in children with chronic bronchitis is lower as compared to those without based on the given data at 5% level.