Marriages in the United States In 1960 676 of the US populat

Marriages in the United States. In 1960, 67.6% of the U.S. population (aged 14 and over) was married. A random sample of 600 Americans in 2011 indicated that 312 were married. estimate the true proportion of married Americans with 99% confidence. assume the varibale is normaly disturbuted.

Solution

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)=312
Sample Size(n)=600
Sample proportion = x/n =0.52
Confidence Interval = [ 0.52 ±Z a/2 ( Sqrt ( 0.52*0.48) /600)]
= [ 0.52 - 2.58* Sqrt(0) , 0.52 + 2.58* Sqrt(0) ]
= [ 0.467,0.573]