Each year more than 1 million heart patients undergo an angioplasty. The benefit

Question

Each year more than 1 million heart patients undergo an angioplasty. The benefits of an angioplasty were challenged in a recent study of 1145 randomly selected patients (2007 Annual Conference of the American College of Cardiology, New Orleans). All the patients had substantial blockage of the arteries, but were medically stable. All were treated with medication such as aspirin and betablockers, and had an angioplasty. After five years, the researchers found that 211 of the 1145 patients had subsequent heart attacks.

(a) Identify and define the parameter of interest.

(b) Identify the value of the statistic of interest in this example.

(c) There is evidence that the population proportion of patients that have substantial blockage of the arteries, but were medically stable, that had subsequent heart attacks is 0.177. Conduct the appropriate test at the = 0.05 level of significance to determine if the proportion of patients with substantial blockage that receive an angioplasty is different than 0.177. Make to show all steps of your hypothesis test.

Explanation / Answer

a) The population proportion of patients with substantial blockage that receive an angioplasty.

******************

b) The sample proportion of patients with substantial blockage that receive an angioplasty.

********************

c)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.177
Ha:   p   =/=   0.177
As we see, the hypothesized po =   0.177      

Getting the point estimate of p, p^,          
          
p^ = x / n = 211/1145 =   0.184279476      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.011279343      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    0.6453812      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.518680184      

significance level =    0.05      

As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Hence, there is no significant evidence ta 0.05 level that the proportion of patients with substantial blockage that receive an angioplasty is different than 0.177. [CONCLUSION]

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