Answer:
<em> 98% of confidence interval for the true population</em>
<em>(0.6326 , 0.7674)</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given sample size 'n' = 250</em>
She surveys 250 individuals and finds that 175 have taken a drug test for work.
<em>sample proportion </em>
![p = \frac{x}{n} = \frac{175}{250} =0.7](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7Bx%7D%7Bn%7D%20%3D%20%5Cfrac%7B175%7D%7B250%7D%20%3D0.7)
<em>level of significance ∝ = 0.05</em>
<em> 98% of confidence interval for the true population is determined by</em>
![(p^{-} - Z_{0.02} \sqrt{\frac{p(1-p)}{n} } ,p +Z_{0.02} \sqrt{\frac{p(1-p)}{n} } )](https://tex.z-dn.net/?f=%28p%5E%7B-%7D%20-%20Z_%7B0.02%7D%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%2Cp%20%2BZ_%7B0.02%7D%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%29)
<em>Z₀.₀₂ = 2.326</em>
<u><em>Step(ii):-</em></u>
<em> 98% of confidence interval for true population is determined by</em>
![(0.7 - 2.326\sqrt{\frac{0.7(1-0.7)}{250} } ,0.7 + 2.326 \sqrt{\frac{0.7(1-0.7)}{250} } )](https://tex.z-dn.net/?f=%280.7%20-%202.326%5Csqrt%7B%5Cfrac%7B0.7%281-0.7%29%7D%7B250%7D%20%7D%20%2C0.7%20%2B%202.326%20%5Csqrt%7B%5Cfrac%7B0.7%281-0.7%29%7D%7B250%7D%20%7D%20%29)
<em>( 0.7 - 0.0674 , 0.7 + 0.0674)</em>
<em>(0.6326 , 0.7674)</em>
<u><em>Conclusion:-</em></u>
<em>98% of confidence interval for the true population is determined by</em>
<em>(0.6326 , 0.7674)</em>