De steekproefproportie is \(\hat{p}={82 \over 179}=0{,}458...\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}458...⋅0{,}541... \over 179}}=0{,}037...\)

\(\hat{p}-2\sigma =0{,}458...-2⋅0{,}037...≈0{,}384\text{.}\)

\(\hat{p}+2\sigma =0{,}458...+2⋅0{,}037...≈0{,}533\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([0{,}384; 0{,}533]\text{.}\)

De steekproefproportie is \(\hat{p}=12\%=0{,}12\text{.}\)

\(\sigma =\sqrt{{\hat{p}(1-\hat{p}) \over n}}=\sqrt{{0{,}12⋅0{,}88 \over 172}}=0{,}0247...\)

\(\hat{p}-2\sigma =0{,}12-2⋅0{,}0247...≈0{,}070\text{.}\)

\(\hat{p}+2\sigma =0{,}12+2⋅0{,}0247...≈0{,}170\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval is \([7{,}0\%, 17{,}0\%]\text{.}\)

\(\bar{X}-2⋅{S \over \sqrt{n}}=294-2⋅{36 \over \sqrt{125}}≈288\text{.}\)

\(\bar{X}+2⋅{S \over \sqrt{n}}=294+2⋅{36 \over \sqrt{125}}≈300\text{.}\)

Het \(95\%\text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([288, 300]\text{.}\)

\(\hat{p}={0{,}348+0{,}492 \over 2}=0{,}42\) en \(\text{breedte}=0{,}492-0{,}348=0{,}144\text{.}\)

Los op \(4⋅\sqrt{{0{,}42⋅0{,}58 \over n}}=0{,}144\text{.}\)

Voer in
\(y_1=4⋅\sqrt{{0{,}42⋅0{,}58 \over x}}\)
\(y_2=0{,}144\)
Optie 'intersect' geeft \(x=187{,}962...\)

De steekproefomvang is dus \(188\text{.}\)

\(S=3{,}8\) en \(\text{breedte}=10{,}7-9{,}5=1{,}2\text{.}\)

Los op \(4⋅{3{,}8 \over \sqrt{n}}=1{,}2\text{.}\)

Voer in
\(y_1=4⋅{3{,}8 \over \sqrt{x}}\)
\(y_2=1{,}2\)
Optie 'intersect' geeft \(x=160{,}444...\)

De steekproefomvang is dus \(160\text{.}\)