During a national debate on changes to health care a cable n

During a national debate on changes to health care, a cable news service performs an opinion poll of 640 small-business owners. It shows that 79% of small-business owners do not approve of the changes. (Use z Distribution Table.)

a. Develop a 99% confidence interval for the proportion opposing health care changes. (Round your answers to 4 decimal places.) Confidence interval for the proportion

b. Do majority approve? Yes No

Solution

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.79          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.016100272          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.748528448          
upper bound = p^ + z(alpha/2) * sp =    0.831471552          
              
Thus, the confidence interval is              
              
(   0.748528448   ,   0.831471552   ) [ANSWER]

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b)

YES, as the whole interval is greater than 0.50. [ANSWER, YES]