University:
York University
Course:
AP/ADMS 2320 | Business Statistics
Academic year:

2022
Views:

257

Pages:

2
Author:

Niklas

Population and sample - a sample is a small part of population population= full set of individuals we want to draw conclusions from -sample mean will be different to population mean - different samples have different means X̄ = n∑i=1xi = n(x1+x2+...+xn) Central Limit Theorem central limit theorem = when sample size is large (n>=30), the sampling distribution of the sample mean is very close to normal distribution if pop mean = μ and pop var = σ², the sampling distribution of sample mean = X̄ ~ N(μ, σ²/n) Time taken for bus journey is norm dist with μ=32 mins and σ=10 mins. One week, a sample of 35 buses gave mean of 33.5. n=35, X̄=33.5 sampling dist of X̄ = 33.5 ~ N(32, 10²/35) → X̄ ~ N(32,1.69) z = (X̄-μ) / (σ/√n) = 33.5-32 / (10/√35) = 0.88 ≈ 0.81057 1 - 0.81057 = 0.18943 μ = p σ² = p(1-p) p̂ = (∑i=1^n Yi) / n {sample mean}