De steekproefproportie is \(\hat{p}={62 \over 174}=0{,}356...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}356...⋅0{,}643... \over 174}}=0{,}036...\)

\(\hat{p}-2\sigma =0{,}356...-2⋅0{,}036...≈0{,}284\text{.}\)

\(\hat{p}+2\sigma =0{,}356...+2⋅0{,}036...≈0{,}429\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}284; 0{,}429]\text{.}\)

De steekproefproportie is \(\hat{p}=23\%=0{,}23\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}23⋅0{,}77 \over 157}}=0{,}0335...\)

\(\hat{p}-2\sigma =0{,}23-2⋅0{,}0335...≈0{,}163\text{.}\)

\(\hat{p}+2\sigma =0{,}23+2⋅0{,}0335...≈0{,}297\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([16{,}3\%; 29{,}7\%]\text{.}\)

\(\bar{X}-2⋅{S \over \sqrt{n}}=3{,}31-2⋅{0{,}62 \over \sqrt{211}}≈3{,}22\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=3{,}31+2⋅{0{,}62 \over \sqrt{211}}≈3{,}40\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([3{,}22; 3{,}40]\text{.}\)

\(\hat{p}={0{,}352+0{,}488 \over 2}=0{,}42\) en \(\text{breedte}=0{,}488-0{,}352=0{,}136\text{.}\)

Los op \(4⋅\sqrt{{0{,}42⋅0{,}58 \over n}}=0{,}136\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}42⋅0{,}58 \over x}}\)
\(y_2=0{,}136\)
Optie 'intersect' geeft \(x=210{,}726...\)

De steekproefomvang is dus \(211\text{.}\)

\(S=9{,}4\) en \(\text{breedte}=24{,}8-22{,}4=2{,}4\text{.}\)

Los op \(4⋅{9{,}4 \over \sqrt{n}}=2{,}4\text{.}\)

Voer in
\(y_1=4⋅{9{,}4 \over \sqrt{x}}\)
\(y_2=2{,}4\)
Optie 'intersect' geeft \(x=245{,}444...\)

De steekproefomvang is dus \(245\text{.}\)