20 A Royal Society for the Prevention of cruelty to Animals

20. A Royal Society for the Prevention of cruelty to Animals (RSPCA) survey of 200 randomly chosen Australian pet owners found that 10 said that they had met their partner through owning the pet. Find the 95% confident interval for the proportion of Australian pet owners who fins love through their pets (Use Agrest-Coul).

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.05          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.015411035          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.019794926          
upper bound = p^ + z(alpha/2) * sp =    0.080205074          
              
Thus, the confidence interval is              
              
(   0.019794926   ,   0.080205074   ) [ANSWER]