Question

1. You are involved in a study of the relationship between smoking and serum cholesterol concentrations of high-density lipoprotein cholesterol (HDL-C), the following data were collected from samples of adult males who were nonsmokers, light smokers, moderate smokers, and heavy smokers. You wish to know if these data provide sufficient evidence to indicate that the four populations differ with respect to mean serum concentration of HDL-C. Let the probability of committing a type I error be 0.05. If an overall significant difference is found, determine which pairs of individual sample means are significant different.

Non smokers	Light Smokers	ModerateSmokers	HeavySmokers
12	9	5	3
10	8	4	2
11	5	7	1
13	9	9	5
9	9	5	4
9	10	7	6
12	8	6	2

Answer 1

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

Non smokers	Light Smokers	ModerateSmokers	HeavySmokers
12	9	5	3
10	8	4	2
11	5	7	1
13	9	9	5
9	9	5	4
9	10	7	6
12	8	6	2
	Mean	n	Std. Dev
	10.9	7	1.57	Non smokers
	8.3	7	1.60	Light Smokers
	6.1	7	1.68	ModerateSmokers
	3.3	7	1.80	HeavySmokers
	7.1	28	3.24	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	216.86	3	72.286	26.06	1.01E-07
Error	66.57	24	2.774
Total	283.43	27
Post hoc analysis
p-values for pairwise t-tests
		HeavySmokers	ModerateSmokers	Light Smokers	Non smokers
		3.3	6.1	8.3	10.9
HeavySmokers	3.3
ModerateSmokers	6.1	.0038
Light Smokers	8.3	8.81E-06	.0241
Non smokers	10.9	1.05E-08	1.97E-05	.0081
Tukey simultaneous comparison t-values (d.f. = 24)
		HeavySmokers	ModerateSmokers	Light Smokers	Non smokers
		3.3	6.1	8.3	10.9
HeavySmokers	3.3
ModerateSmokers	6.1	3.21
Light Smokers	8.3	5.62	2.41
Non smokers	10.9	8.50	5.30	2.89
critical values for experimentwise error rate:
		0.05	2.76
		0.01	3.47

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 four populations differ with respect to mean serum concentration of HDL-C.

There is a significant difference between Non-smokers and HeavySmokers.

There is a significant difference between Light Smokers and HeavySmokers.

There is a significant difference between ModerateSmokers and HeavySmokers.

There is a significant difference between Non-smokers and ModerateSmokers.

There is a significant difference between Light Smokers and ModerateSmokers.

There is a significant difference between Non-smokers and Light Smokers.

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