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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? Group of answer choices
0.094 to 0.146
0.107 to 0.133
0.026 to 0.214
0.068 to 0.12

Respuesta :

Answer:

[tex] 0.12 -1.96*0.013= 0.094[/tex]

[tex] 0.12 +1.96*0.013= 0.146[/tex]

And the best option would be:

0.094 to 0.146

Step-by-step explanation:

For this case we have the following info given:

[tex] \hat p=0.12[/tex] represent the proportion estimated

[tex] SE = 0.013[/tex] represent the standard error

[tex] Confidence =0.95[/tex] represent the confidence level

The confidence interval for the true proportion is given by:

[tex]\hat p \pm z_{\alpha/2} SE[/tex]

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

[tex] 0.12 -1.96*0.013= 0.094[/tex]

[tex] 0.12 +1.96*0.013= 0.146[/tex]

And the best option would be:

0.094 to 0.146

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