A poll surveyed 1000 people age 18 years and older who reside in Hamilton County
ID: 3220394 • Letter: A
Question
A poll surveyed 1000 people age 18 years and older who reside in Hamilton County and found that 55% said they are fans of the Cincinnati Reds. Find SE(p hat) Construct a 90% confidence interval and a 99% confidence interval for the proportion of Reds fans in Hamilton County. What are the margin of errors for these two intervals? Without using a calculator, what do you guess the margin of error is for a 95% confidence interval? How likely is it that the 99% interval did not capture the true value for the proportion of Reds fans in Hamilton county (age 18 years and older)?Explanation / Answer
a.
Standard Error = Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size,
Sample Size(n)=1000
Sample proportion =0.55
Standard Error = Sqrt ( (0.55*0.45) /1000) )
= 0.016
b.
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
Sample Size(n)=1000
Sample proportion = x/n =0.55
Confidence Interval = [ 0.55 ±Z a/2 ( Sqrt ( 0.55*0.45) /1000)]
= [ 0.55 - 1.645* Sqrt(0) , 0.55 + 1.65* Sqrt(0) ]
= [ 0.524,0.576]
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
Sample Size(n)=1000
Sample proportion = x/n =0.55
Confidence Interval = [ 0.55 ±Z a/2 ( Sqrt ( 0.55*0.45) /1000)]
= [ 0.55 - 2.576* Sqrt(0) , 0.55 + 2.58* Sqrt(0) ]
= [ 0.509,0.591]
d.
ME at 0.10
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)=550
Sample Size(n)=1000
Sample proportion =0.55
Margin of Error = Z a/2 * ( Sqrt ( (0.55*0.45) /1000) )
= 1.645* Sqrt(0)
=0.026
ME at 0.01
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)=550
Sample Size(n)=1000
Sample proportion =0.55
Margin of Error = Z a/2 * ( Sqrt ( (0.55*0.45) /1000) )
= 2.576* Sqrt(0)
=0.041