\(\bar{X} - 2 ⋅ {S \over \sqrt{n}} = 3{,}73 - 2 ⋅ {0{,}17 \over \sqrt{149}} ≈ 3{,}70 \text{.}\)

\(\bar{X} + 2 ⋅ {S \over \sqrt{n}} = 3{,}73 + 2 ⋅ {0{,}17 \over \sqrt{149}} ≈ 3{,}76 \text{.}\)

Het \(95\% \text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([3{,}70 ; 3{,}76] \text{.}\)

De steekproefproportie is \(\hat{p} = {114 \over 243} = 0{,}469...\)

\(\sigma = \sqrt{{\hat{p} (1 - \hat{p}) \over n}} = \sqrt{{0{,}469... ⋅ 0{,}530... \over 243}} = 0{,}032...\)

\(\hat{p} - 2 \sigma = 0{,}469... - 2 ⋅ 0{,}032... ≈ 0{,}405 \text{.}\)

\(\hat{p} + 2 \sigma = 0{,}469... + 2 ⋅ 0{,}032... ≈ 0{,}533 \text{.}\)

Het \(95\% \text{-}\)betrouwbaarheidsinterval is \([0{,}405 ; 0{,}533] \text{.}\)

De steekproefproportie is \(\hat{p} = 41\% = 0{,}41 \text{.}\)

\(\sigma = \sqrt{{\hat{p} (1 - \hat{p}) \over n}} = \sqrt{{0{,}41 ⋅ 0{,}59 \over 148}} = 0{,}0404...\)

\(\hat{p} - 2 \sigma = 0{,}41 - 2 ⋅ 0{,}0404... ≈ 0{,}329 \text{.}\)

\(\hat{p} + 2 \sigma = 0{,}41 + 2 ⋅ 0{,}0404... ≈ 0{,}491 \text{.}\)

Het \(95\% \text{-}\)betrouwbaarheidsinterval is \([32{,}9\% ; 49{,}1\%] \text{.}\)

\(\hat{p} = {0{,}402 + 0{,}538 \over 2} = 0{,}47\) en \(\text{breedte} = 0{,}538 - 0{,}402 = 0{,}136 \text{.}\)

Los op \(4 ⋅ \sqrt{{0{,}47 ⋅ 0{,}53 \over n}} = 0{,}136 \text{.}\)

Voer in
\(y_{1} = 4 ⋅ \sqrt{{0{,}47 ⋅ 0{,}53 \over x}}\)
\(y_{2} = 0{,}136\)
Optie 'intersect' geeft \(x = 215{,}484...\)

De steekproefomvang is dus \(215 \text{.}\)

\(S = 1{,}3\) en \(\text{breedte} = 15{,}5 - 15{,}1 = 0{,}4 \text{.}\)

Los op \(4 ⋅ {1{,}3 \over \sqrt{n}} = 0{,}4 \text{.}\)

Voer in
\(y_{1} = 4 ⋅ {1{,}3 \over \sqrt{x}}\)
\(y_{2} = 0{,}4\)
Optie 'intersect' geeft \(x = 169\)

De steekproefomvang is dus \(169 \text{.}\)