Question

With data from the 2009 National Health Interview Survey, the Centers for Disease Control estimated that 9.4% of U.S. children had asthma. Suppose that 12% of a random sample of 500 U.S. poor children have asthma.

We used the estimate from the 2009 National Health Interview Survey to calculate a standard error of 0.013. The data allows the use of a normal model. So we can find an approximate 95% confidence interval for the percentage of all U.S. poor children who have asthma.
Which interval is the approximate 95% confidence interval?
0.107 to 0.133
0.094 to 0.146
0.026 to 0.214
0.068 to 0.12

Answer 1

95% confidence interval is 0.094 to 0.146

Explanation:

Confidence Interval can be calculated using p±ME where

• p is the sample mean of poor children who have asthma. (0.12 or 12%)

• ME is the margin of error from the mean

And margin of error can be stated as ME=z×SE where

• z is the statistic of the 95% confidence level (1.96)
• SE is the standard error (0.013)

Then ME=1.96×0.013≈0.0255

Finally, 95% confidence interval is 0.12±0.0255 ≈ 0.094 to 0.146