De steekproefproportie is \(\hat{p}={36 \over 213}=0{,}169...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}169...⋅0{,}830... \over 213}}=0{,}025...\)

\(\hat{p}-2\sigma =0{,}169...-2⋅0{,}025...≈0{,}118\text{.}\)

\(\hat{p}+2\sigma =0{,}169...+2⋅0{,}025...≈0{,}220\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}118; 0{,}220]\text{.}\)

De steekproefproportie is \(\hat{p}=42\%=0{,}42\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}42⋅0{,}58 \over 119}}=0{,}0452...\)

\(\hat{p}-2\sigma =0{,}42-2⋅0{,}0452...≈0{,}330\text{.}\)

\(\hat{p}+2\sigma =0{,}42+2⋅0{,}0452...≈0{,}510\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([33{,}0\%, 51{,}0\%]\text{.}\)

\(\bar{X}-2⋅{S \over \sqrt{n}}=45{,}9-2⋅{11{,}1 \over \sqrt{105}}≈43{,}7\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=45{,}9+2⋅{11{,}1 \over \sqrt{105}}≈48{,}1\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([43{,}7; 48{,}1]\text{.}\)

\(\hat{p}={0{,}090+0{,}230 \over 2}=0{,}16\) en \(\text{breedte}=0{,}230-0{,}090=0{,}14\text{.}\)

Los op \(4⋅\sqrt{{0{,}16⋅0{,}84 \over n}}=0{,}14\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}16⋅0{,}84 \over x}}\)
\(y_2=0{,}14\)
Optie 'intersect' geeft \(x=109{,}714...\)

De steekproefomvang is dus \(110\text{.}\)

\(S=2{,}16\) en \(\text{breedte}=6{,}47-5{,}91=0{,}56\text{.}\)

Los op \(4⋅{2{,}16 \over \sqrt{n}}=0{,}56\text{.}\)

Voer in
\(y_1=4⋅{2{,}16 \over \sqrt{x}}\)
\(y_2=0{,}56\)
Optie 'intersect' geeft \(x=238{,}040...\)

De steekproefomvang is dus \(238\text{.}\)