Vragen practicum 1 - elearning
Module 5:
s
Standaard deviatie van gemiddelde = standaard error (SE) —>
n
∑ (Xi − X )2
Standaard deviatie (s) =
n−1
Hoe groter de steekproef hoe beter deze het populatie gemiddelde nadert.
De SE van een grote steekproef is kleiner dan de SE van een kleine steekproef.
95% betrouwbaarheidsinterval (CI) = X ± 1,96 × SE
1. Fill in the missing number.
A normally distributed variable has a standard deviation of 16. If we would take several
samples with a size of 64 each, what standard deviation do you expect the sample means will
have?
16 16
Antwoord: = =2
64 8
2. Fill in the missing number. Round to two digits.
What size should a sample from a normal distribution with a known standard deviation (σ =
40) have, to end up with a 95% CI for the population mean with a width of 10?
1. The formula for a 95% CI = x̄ ± …… σ/√n, so the width of the interval equals ……·σ/√n.
2. With a σ of 40, we need at least …… respondents.
Antwoord: 1) 1,96 2 × 1,96 = 3,92
40 3,92 × 40 2
2) 3,92 × ≤ 10 = n ≥ ( ) = n ≥ 245,86 = 246 respondents
n 10
3. Fill in the missing words
What will happen to the width of the 95% CI, if the sample size increases? Consider a known
population standard deviation.
1. The width of the interval will increase/decrease ……, due to the fact that the denominator
will increase/decrease …… .
Antwoord: 1) decrease (afname) increase (toename)
Module 5:
s
Standaard deviatie van gemiddelde = standaard error (SE) —>
n
∑ (Xi − X )2
Standaard deviatie (s) =
n−1
Hoe groter de steekproef hoe beter deze het populatie gemiddelde nadert.
De SE van een grote steekproef is kleiner dan de SE van een kleine steekproef.
95% betrouwbaarheidsinterval (CI) = X ± 1,96 × SE
1. Fill in the missing number.
A normally distributed variable has a standard deviation of 16. If we would take several
samples with a size of 64 each, what standard deviation do you expect the sample means will
have?
16 16
Antwoord: = =2
64 8
2. Fill in the missing number. Round to two digits.
What size should a sample from a normal distribution with a known standard deviation (σ =
40) have, to end up with a 95% CI for the population mean with a width of 10?
1. The formula for a 95% CI = x̄ ± …… σ/√n, so the width of the interval equals ……·σ/√n.
2. With a σ of 40, we need at least …… respondents.
Antwoord: 1) 1,96 2 × 1,96 = 3,92
40 3,92 × 40 2
2) 3,92 × ≤ 10 = n ≥ ( ) = n ≥ 245,86 = 246 respondents
n 10
3. Fill in the missing words
What will happen to the width of the 95% CI, if the sample size increases? Consider a known
population standard deviation.
1. The width of the interval will increase/decrease ……, due to the fact that the denominator
will increase/decrease …… .
Antwoord: 1) decrease (afname) increase (toename)
