Fin Quiz - Smart Summary Study Session 3, Reading 10 PDF

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2020, Study Session # 3, Reading # 10

Sampling & Estimation Ò = Approaches to df = Degrees of Freedom n = Sample Size

SE = Standard Error Ó = Rises RV = Random Variable CI = Class Interval

Methods of Sampling

Simple Random Sampling

Stratified Random Sampling

! Each item of the population under study has equal probability of being selected. ! There is no guarantee of selection of items from a particular category.

Sample A subgroup of population.

Sample Statistic ! It describes the characteristic of a sample. ! Sample statistic itself is a random variable.

Sampling error

Systematic Sampling ! Select every kth number. ! Resulting sample should be approximately random

! Uses a classification system. ! Separates the population into strata (small groups) based on one or more distinguishing characteristics. ! Take random sample from each stratum. ! It guarantees the selection of items from a particular category.

Sample – Corresponding Statistic Population Parameter.

Sampling Distribution Probability distribution of all possible sample statistics computed from a set of equal size samples randomly drawn.

Standard Error (SE) of Sample Mean ! Standard deviation of the distribution of sample means.

sx =

s n

! If s is not known then; Date

Time

Time series

Observations take over equally spaced time interval

Crosssectional

Data

Longitudinal Panel

Observational Units Same

Characteristics

Multiple

Multiple

sx =

s n

! As n Ó;

x

approaches

µ and S.E Ô.

Same

Single point estimate

Student’s T-Distribution ! ! ! ! ! ! !

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Bell shaped. Shape is defined by df df is based on ‘sample size’. Symmetrical about it’s mean. Less peaked than normal distribution. Has fatter tails. More probability in tails i.e., more observations are away from the center of the distribution & more outliers.

All i ht

d

2020, Study Session # 3, Reading # 10

Central Limit Theorem (CLT)

Point Estimate (PE)

For a random sample of size ‘n’ with; ! population mean µ, ! finite variance (population variance divided by sample size) s2, the sampling distribution of

Confidence Interval (CI) Estimates

! Single (sample) value used to estimate population parameter. Σ𝑋 # 𝑋= 𝑛

sample mean x approaches a normal probability distribution with mean ‘µ’ & variance as ‘n’ becomes large.

! Results in a range of values within which actual parameter value will fall. ! PE ±(reliability factor ´ SE). ! a= level of significance. ! 1- a= degree of confidence.

Estimator: Formula used to compute PE.

Desirable properties of an estimator

Properties of CLT ! For n ³ 30 Þ sampling distribution of mean is approx. normal. ! Mean of distribution of all possible

Unbiased Expected value of estimator equals parameter e.g., E(𝑥) = µ i.e, sampling error is zero.

samples = population mean ‘µ’. ! !

Efficient If var (𝑥* ) < var (𝑥+ ) of the same parameter then 𝑥1 is efficient than 𝑥2

CLT applies only when sample is random.

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Consistent As n Ó, value of estimator approaches parameter & sample error approaches ‘0’ e.g., As n Ò µ 𝑥! Ò µ & SE Ò 0

2020, Study Session # 3, Reading # 10

Distribution Non Normal normal P O P O P O P O O P O P O P O P

Variance Known

Unknown

P P O O P P O O

O O P P O O P P

Sample Small Large (n...