# It was observed that 30 of the 100 randomly selected

It was observed that 30 of the 100 randomly selected students smoked. Find the confidence interval estimate of $$\displaystyle{95}\%$$ confidence level for $$\displaystyle\pi$$ ratio of smokers in the population.
a) $$\displaystyle{P}{\left({0.45}{<}{p}{<}{0.78}\right)}={0.95}$$
b) $$\displaystyle{P}{\left({0.11}{<}{p}{<}{0.28}\right)}={0.95}$$
c) $$\displaystyle{P}{\left({0.51}{<}{p}{<}{0.78}\right)}={0.95}$$
d) $$\displaystyle{P}{\left({0.21}{<}{p}{<}{0.59}\right)}={0.95}$$
e) $$\displaystyle{P}{\left({0.21}{<}{p}{<}{0.39}\right)}={0.95}$$

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The $$\displaystyle{95}\%$$ CI is given by
$$\displaystyle{C}{I}={p}\pm{z}_{{{0.05}}}\sqrt{{{\frac{{{p}{q}}}{{{n}}}}}}$$
$$\displaystyle{C}{I}={0.3}\pm{1.96}\sqrt{{{\frac{{{0.3}\times{0.7}}}{{{100}}}}}}$$
$$\displaystyle{C}{I}={\left[{0.21},\ {0.39}\right]}$$
Option (e) is correct.
$$\displaystyle{P}{\left({0.21}{<}{p}{<}{0.39}\right)}={0.95}$$