Question

STATE: 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 55 years old and women at least 65 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 outcome
Treatment	3180	113
Placebo	3168	157

PLAN: Let p1 be the proportion experiencing the primary outcome with the treatment and p2 the proportion without the treatment. Select the correct pair of hypotheses.

?0:?1=?2versus ??:?1>?2.

?0:?1=?2 versus ??:?1<?2.

?0:?1=?2 versus ??:?1≠?2.

None of the options are correct.

SOLVE: Calculate the sample proportions ?̂ 1,?̂ 2, and the pooled sample proportion, p^ . (Enter your answers rounded to four decimals.)

p^1=

p^2=

p^=

Calulate the z statistic. (Enter your answers rounded to two decimals.)

z=

Use the calculated z statistic and Table C to find the correct range for the P‑value. Select it from the options.

0.05 to 0.1

>0.1

0.0005 to 0.001

0.005 to 0.01

CONCLUDE: 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?

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

b.There is not enough information to give a definite response.

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

d.There is virtually no evidence that patients experiencing the primary outcome is different for those receiving the treatment compared to those without.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

p1cap = X1/N1 = 113/3180 = 0.0355

p2cap = X2/N2 = 157/3168 = 0.0496

pcap = (X1 + X2)/(N1 + N2) = (113+157)/(3180+3168) = 0.0425

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.0355-0.0496)/sqrt(0.0425*(1-0.0425)*(1/3180 + 1/3168))
z = -2.78

P-value Approach
P-value = 0.0054

0.005 to 0.01

As P-value < 0.05, reject the null hypothesis.

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