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Chapter 1-9

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York University

Administrative Studies

ADMS 2320

Michael Rochon

Summer

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CHAP 9: Sampling Distribution
- The central limit theorem: n larger-distribution tighter & narrower (more bell-shape)
2 2
- Sampling distribution of the Sample mean: M =M ẍ x ; б =ẍб /n x
P( z = (ẍ-M)/ (б/√n) > ....) - 4 bottles; 1 bottle P(x-M/б);
-Sampling distribution of the proportion: nominal data - p = pˆ = x/n ; E = p ; V = ppˆ-p)/ n pˆ
if both np>5 & n(1-p)>5 then z = (pˆ-p) / [√(p(1-p) /n]
-Sampling Distribution of the ≠ b/w 2 means: Ẍ -Ẍ normal1- b2th are independent & parent normally distributed. If not
normally distributed, but same size >30, so normal. P[( Ẍ -Ẍ ) - (M 1M 2/√ (б /1 +б 2n )>0]21 1 22 2
CHAP 5: Data Collection & Sampling
-Observational study: without controlling any factor >< Experimental: controlling factors might influence value.
- Sampled population = target population.
-3 types of Sampling: 1. Simple Random Sampling: all the same size samples are equally chosen. 2. Stratified Random
Sampling: separate the population to mutually exclusive sets-draw simple random sample from each stratum (can acquire
infor. about whole population, each stratum, relationship among data). 3. Cluster Sampling: is a simple random sample of
groups (useful when diff &costly to ↑ a complete list of population members + population members are widely dispersed
geographically +increase sampling error )
-Sampling error: refer to ≠ b/w sample & population, occur when making a statement about the population based on the
sample taken VS Non- Sampling error: occur due to mistakes made along the process, non response errors, selection bias.
CHAP 8: Continuous Probability Distribution - UNCONTABLE INFINITE z - Normal distribution
- Uniform continuous distribution: f = 1/ ((x)) a ≤ x ≤b ; E = (a+b)/2 ;xV = (b-a) /12 x 2
5
e.g: F x 1/3000 for x=[2000,5000]; P (x≥4000) (x2-x 1 */(b-a) = (5000-4000) 1/3000* .5
-Normal distribution: - б grow - z flat & spread M grow - z ship to right
- P (x=5) = 0 => un-continuous
∑ = 1
-Find normal probability: z = (x - M)/б; e.g: P (-o.5 (2.05 +2.06) /2
=2.055]
CHAP 7: Random variables (2 type: discrete & Continuous) & Discrete probability Distribution
- Discrete variable: has limit, has start, countable, identifiable, definable.
-Discrete probability distribution: a table, formula, or graph that lists all possible values a discrete random variable can
assume.
x Px i
-Requirement for a discrete distribution: 0 ≤ P x ≤1 for ill x ; ∑ i all xix i 1
e.g: P(x≥5) = P(5) + P(6) + P(7 or more) 5 31.3/116
- Developing a probability distribution: Probability calculation techniques can be used
to develop probability distributions. e.g: 20% chance of closing a sell 6 38.6/116
- Describing the population/ Probability distribution:
7 or more 18.8/116(total)
(calculate population mean & variance):
Ex=M=∑ all xii *x ; i =б x E[(x-M) ]=∑(x-M) .Px i 2 i
-Law of expect value & Variance: Ec=c; E =E +c; x+c x
2
E cxE ; x V c0; V =Vx+cV =x V cv x
-Binominal Distributions: -discrete random variable - sill discrete distribution but only have 2 possible outcome "success vs
failure"- everything independent. 3 way to calculate binomial: Tree, Formula: (only for exact value)
n x n-x n 2
P(X=x)=Px=C p (1-px. where C =n!x/ [x!(n-x)!] & Table: Cumulate probability "≤" E =M=np VS V =б xn(1-p) - e.g: x
P (x=18) P (x≤18) (x≤17) P (x≥16) 1- P (x≤15)
CHAP 6: Probability
1 - Assigning probabilities to events: Random experience-outcome is uncertain → can only consider the probability of
occurrence of a certain outcome.
-Sample space: make exhaustive list of all possible outcome → make sure the list outcomes are mutually exclusive
P(A): probability of event

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