Human Cloning In a Gallup Poll 441 of 507 adults said it was

Human Cloning In a Gallup Poll, 441 of 507 adults said it was \"morally wrong\" to clone humans. What proportion of the respondents believed it morally wrong to clone humans? Find a 95% confidence interval for the population proportion who believed it is morally wrong to clone humans. Assume that Gallup used a simple random sample. Find an 80% confidence interval (using a z* of 1,28 if you are calculating by hand). Which interval is wider, and why?

Solution

a)
Mean(x)=447
Sample Size(n)=507
Sample proportion = x/n =0.8817
b)
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)=447
Sample Size(n)=507
Sample proportion = x/n =0.8817
Confidence Interval = [ 0.8817 ±Z a/2 ( Sqrt ( 0.8817*0.1183) /507)]
= [ 0.8817 - 1.96* Sqrt(0.0002) , 0.8817 + 1.96* Sqrt(0.0002) ]
= [ 0.8536,0.9098]

c)
AT 80& CI
Confidence Interval = [ 0.8817 ±Z a/2 ( Sqrt ( 0.8817*0.1183) /507)]
= [ 0.8817 - 1.28* Sqrt(0.0002) , 0.8817 + 1.28* Sqrt(0.0002) ]
= [ 0.8633,0.9001]

d)
Higher the confidence widen the interval