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

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

(0.053 , 0.099)

Explanation:

Explanation:

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

large sample size n=500

Sample proportion 'p' =
`(38)/(500) = 0.076`

q = 1 - p = 1- 0.076 = 0.924

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

`(p-z_(0.95) \sqrt{(pq)/(n) } ,p + z_(0.95)\sqrt{(pq)/(n) } )`

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

(0.076 - 0.023 ,0.076 + 0.023)

(0.053 , 0.099)

Conclusion:-

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

(0.053 , 0.099)