Hypothesis testing with one sample 785 randomly selected sub

Hypothesis testing with one sample:

785 randomly selected subjects who completed four years of college, 144 smoke and 641 do not smoke. Use .01 significance level to test the claim that the rate of smoking amoung those with four years of college is less than 27% rate for the general population.

Use the confidiedence interval approach to solve-

Solution

First, we get the point estimate of the proportion, p^,              
              
p^ = x / n =    0.18343949          
              
Also, we get the standard error of p, sp:              
p = 0.27
              
sp = sqrt[p(1 - p) / n] =    0.015845593          
              
Now, for the critical z,              

alpha =   0.01          

Thus, z(alpha) =    2.326347874          

Thus,              
              
      
upper bound = p^ + z(alpha) * sp =    0.220301851          

p < 0.220301851. [UPPER CONFIDENCE INTERVAL]

Thus, as this interval does not include 0.27, then there is significant evidence that the rate of smoking amoung those with four years of college is less than 27% rate for the general population. [CONCLUSION]