Of 1000 randomly selected cases of lung cancer 845 resulted

Of 1000 randomly selected cases of lung cancer, 845 resulted in death within 10 years. Construct a 95% two-sided confidence interval on the death rate from lung cancer. Use a z-score rounded to 2 decimal places.
Round your answers to 3 decimal places.
(a) Calculate the estimated proportion of lung cancer deaths

p =

( b) Calculate the 95% CI on the death rate from cancer.

( ______________ p ____________ )

Solution

A)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.845       [ANSWER]

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b)  
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.011444431          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.96          
Thus,              
Margin of error = z(alpha/2)*sp =    0.022431085          
lower bound = p^ - z(alpha/2) * sp =   0.822568915          
upper bound = p^ + z(alpha/2) * sp =    0.867431085          
              
Thus, the confidence interval is              
              
(   0.822568915   ,   0.867431085   ) [ANSWER]