Question

These are the results of a health experiment that investigated effectiveness of aspirin of reducing heart attacks. This was a placebo eonctrolled study where 22, 071 male doctors in the United States were given either 325 mg or aspirin or placebo pill every other day for 5 years. The following are the data collected over 5 years.

-List 1. the most appropriate statistical test. 2. null and alternative hypotheses. 3. calculate appropriate test statistic. 4. determine critical value. 5. statistical conclusion.

Group study	Heart attack	no heart attack	total
Aspirin	104	10933	11037
Placebo	189	10845	11034
total	293	21778	22071

Answer 1

1)

Hypothesis Test: Difference of two Proportions              
proportion of heart attacks among taking aspirin vs proportion of heartattack among placebo

2)

let p1 and p2 be proportion of heart attacks among taking aspirin and among placebo group respectively,

Ho:   p1 - p2 =   0
Ha:   p1 - p2 <   0

3)

first sample size,     n1=   11037
number of successes, sample 1 =     x1=   104
proportion success of sample 1 , p̂1=   x1/n1=   0.00942285
      
second sample size,     n2 =    11034
number of successes, sample 2 =     x2 =    189
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.017128874
      
difference in sample proportions,    p̂1 - p̂2 =     -0.007706024
      
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.013275339
      
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.001540777
      
Z-statistic =    (p̂1 - p̂2)/SE =     -5.0014

4)

z-critical value , Z* =        -1.6449 [excel function =normsinv(0.05) ]

5)

since, Z stat < Z-critical value , reject Ho.

conclusion : there is enough evidence to conclude that proportion of heart attacks among taking aspirin is less than that of placebo at α=0.05