Question

Cardiovascular disease is a major cause of death and illness worldwide, with high blood pressure and high LDL cholesterol both being established risk factors. Because most cardiovascular events occur in persons with average risk factors. Because most cardiovascular events occur in persons with average risk and no previous cardiovascular disease history, the present research examined the simultaneous use of both blood pressure reducing drugs and cholesterol reducing drugs on this population, rather than focusing on only those on only those at high risk. Subjects included men at least 5555 years old and women at least 6565 years old without cardiovascular disease who had at least one additional risk factor besides age, such as recent or current smoking, hypertension, or family history of premature coronary heart disease. Those with current cardiovascular disease were excluded from the study. Subjects were randomly assigned to the treatment (cholesterol and blood pressure reducing drugs) or a placebo, and the number suffering the primary outcome of a fatal cardiovascular event, a nonfatal myocardial infarction or a nonfatal stroke, were observed. Provided are the results for the two groups over the course of the study:Group Sample size Number experiencing primary outcomeTreatment 31803180 113113Placebo 31683168 157157PLAN: Let p1p1 be the proportion experiencing the primary outcome with the treatment and p2p2 the proportion without the treatment. Select the correct pair of hypotheses.None of the options are correct.H0:p1=p2H0:p1=p2 versus H????:p1≠p2Ha:p1≠p2 .H0:p1=p2H0:p1=p2 versus H????:p1>p2Ha:p1>p2 .H0:p1=p2H0:p1=p2 versus H????:p10.1>0.10.005 to 0.010.005 to 0.01CONCLUDE: How strong is the evidence that the proportion of the subjects experiencing the primary outcome in the treatment group differs from that of those who were in the control group?There is not enough information to give a definite response.There is strong evidence that patients experiencing the primary outcome is higher for those receiving the treatment compared to those without.There is virtually no evidence that patients experiencing the primary outcome is different for those receiving the treatment compared to those without.There is strong evidence that patients experiencing the primary outcome is different for those receiving the treatment compared to those without.

Answer 1

Null and alternative hypotheses:

H0: p1 = p2

H1: p1 ≠ p2

To find the sample proportions, we have the following:

`p'1 = (x_1)/(n_1) = (113)/(3180) = 0.0355`

`p'2 = (x_2)/(n_2) = (157)/(3168) = 0.0495`

`p' = ((x_1 + x_2)/(n_1 + n_2) = (113 + 157)/(3180 + 3168) = 0.0425`

Calculate Z statistics:

`z = \frac{(p1 -p2)}{\sqrt{(p'(1-p')*((1)/(n1)+ (1)/(n2))}}`

`= \frac{(0.0355 - 0.0495)}{\sqrt{(0.0425*(1-0.0425) * ((1)/(3180) + (1)/(3168))}} = -2.764`

Z = -2.764

P-value = 0.00285

The pvalue is low.

Since the pvalue is low, reject null hypothesis, H0.

Conclusion:

There is strong evidence that patients experiencing the primary outcome is different for those receiving the treatment compared to those without