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-BARSIC- [3]
3 years ago
10

With data from the 2009 National Health Interview Survey, the Centers for Disease Control estimated that 9.4% of U.S. children h

ad 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? Group of answer choices
0.094 to 0.146
0.107 to 0.133
0.026 to 0.214
0.068 to 0.12
Mathematics
1 answer:
egoroff_w [7]3 years ago
5 0

Answer:

0.12 -1.96*0.013= 0.094

0.12 +1.96*0.013= 0.146

And the best option would be:

0.094 to 0.146

Step-by-step explanation:

For this case we have the following info given:

\hat p=0.12 represent the proportion estimated

SE = 0.013 represent the standard error

Confidence =0.95 represent the confidence level

The confidence interval for the true proportion is given by:

\hat p \pm z_{\alpha/2} SE

And for 95% of confidence the critical value is z_{\alpha/2}= 1.96 and replacing we got:

0.12 -1.96*0.013= 0.094

0.12 +1.96*0.013= 0.146

And the best option would be:

0.094 to 0.146

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