During a national debate on changes to health care, a cable news service perform

Question

During a national debate on changes to health care, a cable news service performs an opinion poll of 450 small-business owners. It shows that 48% of small-business owners do not approve of the changes.

a. Develop a 90% confidence interval for the proportion opposing health care changes. (Round your answers to 4 decimal places.)

b. Do the majority approve? Yes or no?

During a national debate on changes to health care, a cable news service performs an opinion poll of 450 small-business owners. It shows that 48% of small-business owners do not approve of the changes.

Explanation / Answer

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
No. of success(x)=216
Sample Size(n)=450
Sample proportion = x/n =0.48
Confidence Interval = [ 0.48 ±Z a/2 ( Sqrt ( 0.48*0.52) /450)]
= [ 0.48 - 1.645* Sqrt(0.001) , 0.48 + 1.65* Sqrt(0.001) ]
= [ 0.441,0.519]

b.we support the claim majority approved

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