Answer:
The 95% confidence interval for the proportion of U.S. asthmatics that are allergic to sulfites
( 0.05281 , 0.0991)
Step-by-step 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 = [tex]p= \frac{38}{500} = 0.076[/tex]
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
[tex](p-1.96\sqrt{\frac{pq}{n} } ,p+1.96\sqrt{\frac{pq}{n} } )[/tex]
[tex](0.076-1.96\sqrt{\frac{0.076X0.924}{500} } ,0.076+1.96\sqrt{\frac{0.076X0.924}{500} } )[/tex]
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)
