A researcher collected blood cholesterol levels of men in three different socioe

Question

A researcher collected blood cholesterol levels of men in three different socioeconomic groups labeled I, II, and III to study whether there is a significant difference between the mean blood cholesterol of the three groups. The data are provided below.

I        II     III

403 312 403

311 222 244

269 302 353

336 420 235

259 420 319

1. What test should the researcher use for the study?

2. Write down the null hypothesis.

3. What's the degrees of freedom for the between group variation?

4. What's the degrees of freedom for the within group variation? 5. What test should be used to compare the mean cholesterol levels between the three groups? 6. What are the assumptions behind the analysis?

Explanation / Answer

Solution:

One way ANOVA

A researcher collected blood cholesterol levels of men in three different socioeconomic groups labelled I, II, and III to study whether there is a significant difference between the mean blood cholesterol of the three groups. The data are provided below.

I

II

III

403

312

403

311

222

244

269

302

353

336

420

235

259

420

319

Solution:

Here, the researcher should use the one way analysis of variance or ANOVA test for this study.

Solution:

The null hypothesis for this study is given as below:

Null hypothesis: H0: There is no any significant difference between the mean blood cholesterol of the three groups I, II and III.

Solution:

The degrees of freedom for the between group variation is given as 3 – 1 = 2.

Solution:

The degrees of freedom for the within group variation is given as 15 – (2+1) = 15 – 3 = 12

Solution:

Here, we need to use the one way analysis of variance for comparing the mean cholesterol levels between the three groups. The test is given as below:

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

I

5

1578

315.6

3362.8000

II

5

1676

335.2

7209.2000

III

5

1554

310.8

5139.2000

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

1670.9333

2

835.4667

0.1595

0.8543

3.8853

Within Groups

62844.8000

12

5237.0667

Total

64515.7333

14

Level of significance

0.05

Solution:

We assume that the observations from each group should be from single population. Also, we assume that the observations follow an approximately normal distribution.

I

II

III

403

312

403

311

222

244

269

302

353

336

420

235

259

420

319

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