= Solution
A <sensitivity analysis for unit and item nonresponse> asks how much the population estimate and substantive conclusions change when the untestable response assumptions are weakened. Vary plausible virginity probabilities among the missing groups, and vary the unknown embarrassment mixture among unit nonresponders; identify combinations which materially alter the estimate or reverse a conclusion.
For example, let $a,b$ be the positive probabilities among embarrassed and nonembarrassed item nonresponders, let $q$ be the embarrassed fraction among unit nonresponders, and let $c,d$ be their corresponding positive probabilities. The sensitivity estimate is
$$
\boxed{p_{\mathrm{all}}(a,b,c,d,q)=\frac{68+100a+50b+300[qc+(1-q)d]}{1050}.}
$$
The nominal assumptions set $a=c=0.18$, $b=d=0.08$ and $q=0.4$, reproducing $12\%$. Different choices model outcome-dependent refusal or a changed mixture. Sampling <confidence intervals> measure a different uncertainty and should also be reported where appropriate; they do not validate the missingness assumptions.
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