Question

A 2006 report of the U.S. Surgeon General states that "there is no risk-free level of exposure to secondhand smoke. Nonsmokers exposed to secondhand smoke at home or work increase their risk of developing heart disease by 25 to 30 percent and lung cancer by 20 to 30 percent. The finding is of major public health concern due to the fact that nearly half of all nonsmoking Americans are still regularly exposed to secondhand smoke."

Consider the following data from the U.S. Department of Health and Human Services, National Center for Health Statistics, Third National Health and Nutrition Examination Survey. All values are measured levels of serum cotinine (in ng/ml), a metabolite of nicotine—when nicotine is absorbed by the body, cotinine in produced.

Smokers ETS No ETS

1 164 210 121 384 1 0 1 0 0 0 309

35 250 103 1 4 2 0 74 0 0 0 0

130 173 253 32 0 19 3 13 1 0 1 0

123 289 86 313 0 17 1 197 0 0 0 244

0 198 44 266 0 45 178 1 0 0 0 0

112 245 222 208 0 1 51 1 9 0 0 0

234 265 87 3 3 1 1 1 0 0 0 0

167 227 284 491 551 1 0 3 0 0 0 0

131 17 277 290 69 13 2 0 0 90 0 0

477 48 149 173 543 1 0 241 0 0 0 0

Smokers = subjects reported tobacco use

ETS = nonsmokers exposed to environmental tobacco smoke at home or work

No ETS = nonsmokers with no exposure to environmental tobacco smoke at home or work

Use a Kruskal-Wallis test with a 0.05 significance level to test the claim that the median cotinine levels are not all equal for these three groups. What do the results suggest about secondhand smoke?

Answer 1

The hypothesis being tested is:

H0: The median cotinine levels are all equal for these three groups

Ha: The median cotinine levels are not equal for at least one of these three groups

Median	n	Avg. Rank
170.00	40	90.74	Smokers ETS
1.50	40	59.84	No
0.00	40	30.93	ETS
2.00	120		Total
		62.351	H (corrected for ties)
		2	d.f.
		2.89E-14	p-value

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the median cotinine levels are not all equal for these three groups.

Smokers' ETS cotinine production level is the highest.

Smokers ETS	No	ETS
1	384	0
35	4	0
130	0	1
123	0	0
0	0	0
112	0	9
234	3	0
167	551	0
131	69	0
477	543	0
164	1	0
250	2	0
173	19	0
289	17	0
198	45	0
245	1	0
265	1	0
227	1	0
17	13	90
48	1	0
210	0	0
103	0	0
253	3	1
86	1	0
44	178	0
222	51	0
87	1	0
284	0	0
277	2	0
149	0	0
121	1	309
1	74	0
32	13	0
313	197	244
266	1	0
208	1	0
3	1	0
491	3	0
290	0	0
173	241	0