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 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 focus 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 or a nonfatal myocardial infarction or a nonfatal stroke were observed. The results for the two groups over the course of the study are given in the table.  Group Sample size Number Experiencing Primary Outcome  Treatment 3180 113  Placebo 3168 157 How strong is the evidence that the proportion of subjects experiencing the primary outcome in the treatment group differs from that of those who were in the control group? Follow the four‑step process. Salim Yusuf et al., "Blood‑pressure and cholesterol lowering in persons without cardiovascular disease," New England Journal of Medicine, 374 (2016), pp. 2032–2043.   SOLVE: Calculate the sample proportions, ?̂ 1 and ?̂ 2,, and the pooled sample proportion, ?̂ . Give your answers to four decimal places. ?̂ 1=     ?̂ 2=     ?̂ =   Compute the test statistic ?. Give your answer to two decimal places. ?=     Using Table A, find the range for the ?-value.the P-value. 0.010.05

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 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 focus 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 or a nonfatal myocardial infarction or a nonfatal stroke were observed. The results for the two groups over the course of the study are given in the table.

How strong is the evidence that the proportion of subjects experiencing the primary outcome in the treatment group differs from that of those who were in the control group? Follow the four‑step process.

SOLVE: Calculate the sample proportions, ?̂ 1 and ?̂ 2,, and the pooled sample proportion, ?̂ . Give your answers to four decimal places.