1Construct a confidence interval of the population proportio

1.Construct a confidence interval of the population proportion at a given level of confidence.

X=540, n=1200, 94% confidence

The upper bound of the confidence interval is.____

The Lower bound of the confidence interval is.____

(Round to the nearest thousandth as needed)

2. A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sampler should be obtained if he wishes the estimate to be within 3% points with 99% confidence if.

He uses a previous estimate of 34% n=____

He does not use any prior estimates n=______

Solution

a)
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)=540
Sample Size(n)=1200
Sample proportion = x/n =0.45
Confidence Interval = [ 0.45 ±Z a/2 ( Sqrt ( 0.45*0.55) /1200)]
   = [ 0.45 - 1.88* Sqrt(0.0002) , 0.45 + 1.88* Sqrt(0.0002) ]
= [ 0.423,0.477]

b)
He uses a previous estimate of 34% n
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.58
Samle Proportion = 0.34
ME = 0.03
n = ( 2.58 / 0.03 )^2 * 0.34*0.66
= 1659.6624 ~ 1660

WITHOUT USE OF PREVIOUS
Samle Proportion = 0.5
ME = 0.03
n = ( 2.58 / 0.03 )^2 * 0.5*0.5
= 1849 ~ 1849