Question

Stents vs. Surgery
A medical study wanted to test the claim that stent implantation was more effective than surgery for clearing neck arteries of plaque. 38.6% of the patients treated with surgery had suffered a heart attack, a stroke, or died within three years of their surgery. 41 of the 143 patients treated with stent implantation had suffered a heart attack, a stroke, or died within three years of their surgery. Test the medical study's claim at a 0.01 level of significance.

1. Null and alternate hypothesis in both symbolic and sentence form.
2. Significance & p-value.
3. Conclusion with interpretation of results.
4. EXTRA CREDIT Interpretation of possible Type I or Type II error.

Answer 1

a)

Ho :   p =    0.386
H1 :   p >   0.386

null hypothesis: stent implantation was not more effective than surgery for clearing neck arteries of plaque

alternate hypothesis:stent implantation was more effective than surgery for clearing neck arteries of plaque

b)

Level of Significance,   α =    0.01      
Number of Items of Interest,   x =   41      
Sample Size,   n =    143      
              
Sample Proportion ,    p̂ = x/n =    0.2867   
              
Standard Error ,    SE = √( p(1-p)/n ) =    0.040710817      
              
Z Test Statistic =    Z = ( p̂-p)/SE =    -2.438828801      
              
  
p-Value   =   0.9926  
c)

Conclusion:     p-value>α , do not reject null hypothesis

there is not enough evidence to support claim at α=0.01

d)

type I error :

concluded that stent implantation was more effective than surgery for clearing neck arteries of plaque,in actual it is not

type II error:

concluded that stent implantation was not more effective than surgery for clearing neck arteries of plaque,in actual it is more effective