De steekproefproportie is \(\hat{p} = {55 \over 116} = 0{,}474...\)

\(\sigma = \sqrt{{\hat{p} (1 - \hat{p}) \over n}} = \sqrt{{0{,}474... ⋅ 0{,}525... \over 116}} = 0{,}046...\)

\(\hat{p} - 2 \sigma = 0{,}474... - 2 ⋅ 0{,}046... ≈ 0{,}381 \text{.}\)

\(\hat{p} + 2 \sigma = 0{,}474... + 2 ⋅ 0{,}046... ≈ 0{,}567 \text{.}\)

Het \(95\% \text{-}\)betrouwbaarheidsinterval is \([0{,}381 ; 0{,}567] \text{.}\)

De steekproefproportie is \(\hat{p} = 28\% = 0{,}28 \text{.}\)

\(\sigma = \sqrt{{\hat{p} (1 - \hat{p}) \over n}} = \sqrt{{0{,}28 ⋅ 0{,}72 \over 227}} = 0{,}0298...\)

\(\hat{p} - 2 \sigma = 0{,}28 - 2 ⋅ 0{,}0298... ≈ 0{,}220 \text{.}\)

\(\hat{p} + 2 \sigma = 0{,}28 + 2 ⋅ 0{,}0298... ≈ 0{,}340 \text{.}\)

Het \(95\% \text{-}\)betrouwbaarheidsinterval is \([22{,}0\% , 34{,}0\%] \text{.}\)

\(\bar{X} - 2 ⋅ {S \over \sqrt{n}} = 892 - 2 ⋅ {133 \over \sqrt{152}} ≈ 870 \text{.}\)

\(\bar{X} + 2 ⋅ {S \over \sqrt{n}} = 892 + 2 ⋅ {133 \over \sqrt{152}} ≈ 914 \text{.}\)

Het \(95\% \text{-}\)betrouwbaarheidsinterval voor het populatiegemiddelde is \([870 , 914] \text{.}\)

\(\hat{p} = {0{,}400 + 0{,}580 \over 2} = 0{,}49\) en \(\text{breedte} = 0{,}580 - 0{,}400 = 0{,}18 \text{.}\)

Los op \(4 ⋅ \sqrt{{0{,}49 ⋅ 0{,}51 \over n}} = 0{,}18 \text{.}\)

Voer in
\(y_{1} = 4 ⋅ \sqrt{{0{,}49 ⋅ 0{,}51 \over x}}\)
\(y_{2} = 0{,}18\)
Optie 'intersect' geeft \(x = 123{,}407...\)

De steekproefomvang is dus \(123 \text{.}\)

\(S = 21{,}4\) en \(\text{breedte} = 91{,}9 - 83{,}9 = 8{,}0 \text{.}\)

Los op \(4 ⋅ {21{,}4 \over \sqrt{n}} = 8{,}0 \text{.}\)

Voer in
\(y_{1} = 4 ⋅ {21{,}4 \over \sqrt{x}}\)
\(y_{2} = 8{,}0\)
Optie 'intersect' geeft \(x = 114{,}49\)

De steekproefomvang is dus \(114 \text{.}\)