De steekproefproportie is \(\hat{p}={57 \over 212}=0{,}268...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}268...⋅0{,}731... \over 212}}=0{,}030...\)

\(\hat{p}-2\sigma =0{,}268...-2⋅0{,}030...≈0{,}208\text{.}\)

\(\hat{p}+2\sigma =0{,}268...+2⋅0{,}030...≈0{,}330\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}208; 0{,}330]\text{.}\)

De steekproefproportie is \(\hat{p}=15\%=0{,}15\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}15⋅0{,}85 \over 235}}=0{,}0232...\)

\(\hat{p}-2\sigma =0{,}15-2⋅0{,}0232...≈0{,}103\text{.}\)

\(\hat{p}+2\sigma =0{,}15+2⋅0{,}0232...≈0{,}197\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([10{,}3\%; 19{,}7\%]\text{.}\)

\(\bar{X}-2⋅{S \over \sqrt{n}}=1{,}74-2⋅{0{,}15 \over \sqrt{149}}≈1{,}72\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=1{,}74+2⋅{0{,}15 \over \sqrt{149}}≈1{,}76\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([1{,}72; 1{,}76]\text{.}\)

\(\hat{p}={0{,}288+0{,}452 \over 2}=0{,}37\) en \(\text{breedte}=0{,}452-0{,}288=0{,}164\text{.}\)

Los op \(4⋅\sqrt{{0{,}37⋅0{,}63 \over n}}=0{,}164\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}37⋅0{,}63 \over x}}\)
\(y_2=0{,}164\)
Optie 'intersect' geeft \(x=138{,}667...\)

De steekproefomvang is dus \(139\text{.}\)

\(S=2{,}37\) en \(\text{breedte}=7{,}39-6{,}59=0{,}80\text{.}\)

Los op \(4⋅{2{,}37 \over \sqrt{n}}=0{,}80\text{.}\)

Voer in
\(y_1=4⋅{2{,}37 \over \sqrt{x}}\)
\(y_2=0{,}80\)
Optie 'intersect' geeft \(x=140{,}422...\)

De steekproefomvang is dus \(140\text{.}\)