De steekproefproportie is \(\hat{p}={41 \over 182}=0{,}225...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}225...⋅0{,}774... \over 182}}=0{,}030...\)

\(\hat{p}-2\sigma =0{,}225...-2⋅0{,}030...≈0{,}163\text{.}\)

\(\hat{p}+2\sigma =0{,}225...+2⋅0{,}030...≈0{,}287\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}163; 0{,}287]\text{.}\)

De steekproefproportie is \(\hat{p}=39\%=0{,}39\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}39⋅0{,}61 \over 168}}=0{,}0376...\)

\(\hat{p}-2\sigma =0{,}39-2⋅0{,}0376...≈0{,}315\text{.}\)

\(\hat{p}+2\sigma =0{,}39+2⋅0{,}0376...≈0{,}465\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([31{,}5\%; 46{,}5\%]\text{.}\)

\(\bar{X}-2⋅{S \over \sqrt{n}}=30{,}8-2⋅{2{,}5 \over \sqrt{200}}≈30{,}4\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=30{,}8+2⋅{2{,}5 \over \sqrt{200}}≈31{,}2\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([30{,}4; 31{,}2]\text{.}\)

\(\hat{p}={0{,}258+0{,}382 \over 2}=0{,}32\) en \(\text{breedte}=0{,}382-0{,}258=0{,}124\text{.}\)

Los op \(4⋅\sqrt{{0{,}32⋅0{,}68 \over n}}=0{,}124\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}32⋅0{,}68 \over x}}\)
\(y_2=0{,}124\)
Optie 'intersect' geeft \(x=226{,}430...\)

De steekproefomvang is dus \(226\text{.}\)

\(S=61\) en \(\text{breedte}=621-601=20\text{.}\)

Los op \(4⋅{61 \over \sqrt{n}}=20\text{.}\)

Voer in
\(y_1=4⋅{61 \over \sqrt{x}}\)
\(y_2=20\)
Optie 'intersect' geeft \(x=148{,}84\)

De steekproefomvang is dus \(149\text{.}\)