Q8 In a survey of 102 doctors only 47 knew the generic name

Q8. In a survey of 102 doctors only 47 knew the generic name for the drug methadone. Does this provide strong evidence for concluding that fewer than half of all physicians know the generic name for methadone? Carry out a suitable test of hypotheses using a = .01 and using the P-value method.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.5
Ha:   p   <   0.5

As we see, the hypothesized po =   0.5      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.460784314      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.049507377      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -0.792118034      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.214145928      

significance level =    0.01      

As p > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

There is no significant evidence at 0.01 level that fewer than half of all physicians know the generic name of methadone. [conclusion]