A survey conducted in a large metropolitan area revealed tha

A survey conducted in a large metropolitan area revealed that among high school students 35 percent have, at one time or another, smoked marijuana. If, in a random sample of 150 of these students, only 40 admit to having ever smoked marijuana, what would you conclude?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.35
Ha:   p   =/=   0.35
As we see, the hypothesized po =   0.35      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.266666667      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.038944405      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.139802463      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.032370734      

significance level =    0.05      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.      

Thus, at 0.05 level, there is no significant evidence that the proportion of those who somked marijuana is 35%.