A random sample of n 500 observations from a binomial popul

A random sample of n = 500 observations from a binomial population produced x = 420 successes.

(a) Find a point estimate for p.
p =  

Find the 95% margin of error for your estimator. (Round your answer to three decimal places.)


(b) Find a 90% confidence interval for p. (Round your answers to three decimal places.)
to  

Solution

a)
point estimate for p = 0.84
b)
Margin of Error = Z a/2 Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=420
Sample Size(n)=500
Sample proportion =0.84
Margin of Error = Z a/2 * ( Sqrt ( (0.84*0.16) /500) )
= 1.96* Sqrt(0)
=0.032
c)
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=420
Sample Size(n)=500
Sample proportion = x/n =0.84
Confidence Interval = [ 0.84 ±Z a/2 ( Sqrt ( 0.84*0.16) /500)]
= [ 0.84 - 1.645* Sqrt(0) , 0.84 + 1.65* Sqrt(0) ]
= [ 0.813,0.867]