SOLUTION: 9-8 During a national debate on changes to health care, a cable news service performs an opinion poll of 550 small-business owners. It shows that 70% of small-business owners do n

Question 1202903: 9-8
During a national debate on changes to health care, a cable news service performs an opinion poll of 550 small-business owners. It shows that 70% of small-business owners do not approve of the changes.
a. Compute the 98% confidence interval for the population proportion of small-business owners who do not approve of the changes (Round your answers to 3 decimal places.) ____ and ____
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
.98 confidence interval has a critical z-score of plus or minus 2.32637.
p = .70
1 - p = .30 = q
n = 550 = sample size
s = standard error = sqrt(p * (1 - p) / n) = sqrt(.7 * .3 / 550) = .01954.
z = (x - m) / s
z is the z-score
x is the critical raw score.
m is the mean
s is the standard error
when z = 2.32637, the formula becomes 2.32637 = (x - .7) / .01954.
solve for x to get x = .745457.
when z = -2.32637, the formula becomes -2.32637 = (x - .7) / .01954.
solve for x to get x = .654543.
your 98% confidence interval is .654543 to .745457.
round to 3 decimal places is .655 to .745.
here's what it looks like on a graph.

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