Answer:
A. Margin of error=0.0346
B. Confidence interval=0.4854 to 0.5546
Step-by-step explanation:
A. Computation the margin of error
First step is to calculate the Confidence level using this formula
Confidence level= 1 -α
Where,
α=0.95
Let plug in the formula
Confidence level= 1-0.95
Confidence level= 0.05
Second step is to find Z using this formula
Zα/2
Let plug in the formula
Z= 0.05/2
Z=0.025
Third step is to find the Z score of Z=0.025
Zα/2=1.96
Now let calculate the margin of error using this formula
Margin of error=Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Margin of error=1.96√0.52(1-0.52)/800
Margin of error=1.96√0.52(0.48)/800
Margin of error=1.96√0.2496/800
Margin of error=1.96√0.000312
Margin of error=0.0346
Therefore Margin of error will be 0.0346
B. Computation for the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009
Computation for the boundaries of confidence interval
Using this formula
p- Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Confidence interval=0.52-1.96√0.52(1-0.52)/800
Confidence interval=0.52-1.96√0.52(0.48)/800
Confidence interval=0.52-1.96√0.2496/800
Confidence interval=-0.52-1.96√0.000312
Confidence interval=0.4854
Computation for the boundaries of confidence interval
Using this formula
p+ Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Confidence interval=0.52+1.96√0.52(1-0.52)/800
Confidence interval=0.52+1.96√0.52(0.48)/800
Confidence interval=0.52+1.96√0.2496/800
Confidence interval=-0.52+1.96√0.000312
Confidence interval=0.5546
Therefore the 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009 is 0.4854 to 0.5546
