Question

The following data come from a study that examines the efficacy of saliva cotinine as an indicator for exposure to tobacco smoke. In one part of the study, seven subjects – none of whom were heavy smokers and all of whom had abstained from smoking for at least one week prior to the study- were each required to smoke a single cigarette. Samples of saliva were taken from all individuals 2, 12, 24, and 48 hours after smoking the cigarette. The cotinine levels at 12 hours and at 24 hours are shown below:

Subject	Cotinine levels (nmol/l)
	After 12 hours	After 24 hours
1	73	24
2	58	27
3	67	49
4	93	59
5	33	0
6	18	11
7	147	43

Let u₁₂  represent the population mean cotinine level 12 hours after the cigarette and u₂₄ represent the mean cotinine level 24 hours after smoking. It is believed that u₂₄ must be lower than u₁₂.

SHOW WORK

What are the null and alternative hypotheses?

What type of test statistic can you calculate to test your hypotheses?

Does the data meet all of the assumptions for that test? (show your work)

Test the null hypothesis at the alpha = 0.05 significance level. What can you conclude?

Answer 1

After 12 hours	After 24 hours	Difference
73	24	49
58	27	31
67	49	18
93	59	34
33	0	33
18	11	7
147	43	104

Sample mean of the difference using excel function AVERAGE(), x̅d = 39.4286

Sample standard deviation of the difference using excel function STDEV.S(), sd = 31.3946

Sample size, n = 7

Null and Alternative hypothesis: It is believed that u₂₄ must be lower than u₁₂. so u₁₂ - u₂₄ is greater than 0.

Ho : µd = 0 ; H1 : µd > 0

We will conduct a paired t test statistic.

Assumption:

• The sample is random and independent.
• The data is approximately normally distributed.

Test statistic:

t = (x̅d)/(sd/√n) = (39.4286)/(31.3946/√7) = 3.3228

df = n-1 = 6

Right tailed p-value = T.DIST.RT(3.3228, 6) = 0.0080

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that the population mean cotinine level 24 hours after is lower than the mean cotinine level 12 hours after smoking.