Answer:
<em>90% confidence interval for the proportion of all adults in the city of Darby that are vegetarians</em>
<em>(0.0643075 , 0.0856925)</em>
Step-by-step explanation:
<u><em>Explanation</em></u>
Size of the random sample 'n' = 1613
<em>The proportion of the vegetarian p = 0.075</em>
<em>Level of significance = 0.10</em>
90% confidence interval for the proportion of all adults in the city of Darby that are vegetarians
![(p^{-} - Z_{0.10} \sqrt{\frac{p(1-p)}{n} } , (p^{-} + Z_{0.10} \sqrt{\frac{p(1-p)}{n} })](https://tex.z-dn.net/?f=%28p%5E%7B-%7D%20-%20Z_%7B0.10%7D%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%2C%20%28p%5E%7B-%7D%20%2B%20Z_%7B0.10%7D%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%29)
![(0.075 - 1.645 \sqrt{\frac{0.075(1-0.075)}{1613} } , (0.075 + 1.645 \sqrt{\frac{0.075(1-0.075)}{1613} })](https://tex.z-dn.net/?f=%280.075%20-%20%201.645%20%5Csqrt%7B%5Cfrac%7B0.075%281-0.075%29%7D%7B1613%7D%20%7D%20%2C%20%280.075%20%2B%201.645%20%5Csqrt%7B%5Cfrac%7B0.075%281-0.075%29%7D%7B1613%7D%20%7D%29)
( 0.075 - 1.645 × 0.0065 , 0.075 +1.645 × 0.0065)
( 0.075 -0.0106925 , 0.075+0.0106925)
(0.0643075 , 0.0856925)
<u><em>Final answer</em></u>:-
<em>90% confidence interval for the proportion of all adults in the city of Darby that are vegetarians</em>
<em>(0.0643075 , 0.0856925)</em>
<em></em>