Question

6. The respiratory disturbance index (RDI), which is the number of apneic and hypopneic episodes per hour of sleep, was used as a measure of severity of sleep apnea. An RDI of 5 or more indicates sleep-related breathing disturbances. The RDIs for the females and males samples in a study in US are as follows.

Female				Male
0.1	0.5	0.3	2.3	2.6	19.3	1.4	1.0	0.0	39.2	4.1
2.0	1.4	0.0		0.0	2.1	1.1	5.6	5.0	7.0	2.3
				4.3	7.5	16.5	7.8	3.3	8.9	7.3

At the 1% significance level, do the data provide sufficient evidence to conclude that the female patients are less suffer than male from the apnea disease?

7. An article titled “Hypertension Drug Linked to Cancer”, studies several types of high-blood-pressure drugs and links to cancer. For one type, called calcium-channel blockers, 27 out of 202 elderly patients taking the drug developed cancer. For another type, called beta-blockers, 28 out of 424 other elderly patients developed cancer. At the 1% significance level, do the data provide sufficient evidence to conclude that the probability of getting cancer higher of taking calcium-channel blockers than of taking beta-blockers.

Answer 1

6)

X1 bar	0.942857143 (AVERAGE())	X2 bar	7.265
S1	0.946673374 (STDEV())	S2	9.022036
n1	7	n2	20

F stat = S1^2/S2^2 = 0.011

F critical

FL = 0.1929, FU = 3.1718

F stat < FL, Reject equal variance of null hypothesis (Unequal Variances)

T test:

Hypothesis :		α=	0.01
		df	20.1511
Ho:	μ1​ = μ2
Ha:	μ1​ < μ2
t Critical Value :
tc	-2.527977003	T.INV(α,df)	LEFT
ts	<=	tc	LEFT	To reject
Test :
t	-3.085667307	(X1 bar-X2 bar )/SQRT(S1^2/n1 + S2^2/n2)	Unequal variance
P value :
p	0.002915631	T.DIST(ts,df,TRUE)	LEFT
Decision :
P value	<	α	Reject H0

Conclusion:

The data provide sufficient evidence to conclude that the female patients are less suffer than male from the apnea disease at the 1% significance level

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