Question

Studies have been performed to estimate the percentage of U.S. asthmatics who are allergic to sulfites. In one survey, 38 of 500 randomly selected U.S. asthmatics were found to be allergic to sulfites. Construct a 95% confidence interval for the proportion of U.S. asthmatics that are allergic to sulfites. Round the endpoints to three decimal places.

Answer 1

The 95% confidence interval for the proportion of U.S. asthmatics that are allergic to sulfites

( 0.05281 , 0.0991)

Explanation:

Step:-1

Given sample size is n=500

In one survey, 38 of 500 randomly selected U.S. asthmatics were found to be allergic to sulfites

Proportion of allergic to sulfites =
`p= (38)/(500) = 0.076`

q = 1-p = 1- 0.076 = 0.924

Step:-(ii)

The 95% confidence interval for the proportion of U.S. asthmatics that are allergic to sulfites

`(p-1.96\sqrt{(pq)/(n) } ,p+1.96\sqrt{(pq)/(n) } )`

`(0.076-1.96\sqrt{(0.076X0.924)/(500) } ,0.076+1.96\sqrt{(0.076X0.924)/(500) } )`

on calculation , we get

(0.076 - 0.02319 , 0.076 + 0.02319)

( 0.05281 , 0.0991)

Conclusion:-

The 95% confidence interval for the proportion of U.S. asthmatics that are allergic to sulfites

( 0.05281 , 0.0991)