Lecture 2 - Sampling

Question 1

what is sampling? (definition)

Answer 1

predetermined procedure for selection, withdrawal, preservation, transportation and preparation of portions to be removed from a lot as samples

Question 2

why do sampling?

Answer 2

• using a fraction of population is faster and cheaper
• analyzing a whole population is practically difficult
• gives info about whole population

Question 3

increasing sample size increases…

Answer 3

• accuracy

- also time, cost, sampling methods, logistics of sample handling, analysis and data processing

Question 4

appropriate sampling avoids…

Answer 4

1. consumer risk

2. producer’s risk

Question 5

what is consumer risk?

what is producer’s risk?

Answer 5

risk of accepting defective product

risk of rejecting an acceptable product

Question 6

what are sampling and non-sampling errors?

Answer 6

sampling: arises when sample is not representative of population

non sampling: arises b/c of other reasons (ie environmental error from wrong strage)

Question 7

what is variance?

total variance?

Answer 7

estimate of uncertainty

total variance: function of sum of variances associated w/ each step

Question 8

1. error occuring during sampling?
2. during sample prep?
3. during lab analysis?
4. during data processing?
5. during interpretation?

Answer 8

1. sampling error
2. erroneous sample prep
3. manual or instrumental error
4. erroneous data handling
5. erroneous inference

Question 9

factors that affect choice of sampling plans?

Answer 9

1. purpose of inspection
2. nature of population
3. nature of product
4. nature of test method

Question 10

def of sample?

Answer 10

portion selected from large quantity of material. (general term)
- diff than lab sample

Question 11

def of lab sample?

Answer 11

sample prepared for testing or analysis

Question 12

def of population?

Answer 12

set of all objects in system being investigated

Question 13

def of lot

Answer 13

quantity of bulk material of similar composition whose properties are under study

Question 14

def of batch

Answer 14

quantity of food that is known or assumed to be produced under uniform conditions

batch number should always be noted when sampling foods

Question 15

def of unit

Answer 15

Each of the discrete, identifiable units of food that are suitable for removal from the population as samples and that can be individually described, analyzed or combined (e.g. an apple, a bunch of bananas, a can of beans, a prepared dish).

Question 16

def of homogeneity

Answer 16

degree to which a property or substance is randomly distributed throughout a material.

Question 17

def of increment

Answer 17

An individual portion of material collected by a single operation of a sampling device.
- Increment can be tested individually or combined and tested as a unit.

Question 18

def of increment

Answer 18

An individual portion of material collected by a single operation of a sampling device.
- Increment can be tested individually or combined and tested as a unit.

Question 19

attribute vs variance sampling?

Answer 19

attribute:

• to decide on acceptability of a population based on whether the sample possess a certain characteristic or not
• 2 possible outcomes (conforming or nonconforming –> present or absent)
• sample size must be at least ten times smaller than population size

variance

• estimate quantitatively the amount of substance (ie proteint content or moisture content) or a characteristic (ie color) on a continuous scale
• esterimate obtained from sample is compared w/ an acceptable value

Question 20

manual vs continuous sampling

Answer 20

manual:

• person doing sampling is trained
• picks samples randomly from sample lot

continuous:

• performed mechanically
• less prone to human bias than manual

Question 21

3 criteria used to determine sample size?

Answer 21

1. level of precision (or sampling error): defines desired level of precision when attributes are measured by using the sample
2. level of confidence (or risk): 9% confidence level means 95 out of 100 samples have true population value within the range of precision specified
3. degree of variability among population for attributes being measured: refers to distribution of attributes in population

Question 22

sample size determination can be based on….

Answer 22

1. precision analysis (confidence level)

2. power analysis (power of prediction)

Question 23

Determine the sample size to test the total sugar in a lot of doughnuts with a level of confidence of 95 % and 5% accuracy (precision level). Preliminary test have estimated the average value to be 30 g of sugar per tray. The standard deviation was calculated to be 5g

Answer 23

n = ( (1.96 x 5)/(0.05 x 30) )^2

n=43

Question 24

higher standard deviation means what?

Answer 24

a more heterogeneous sample

thus the sample size must increase

Question 25

equation for calculating sample size when population size is known?

Answer 25

sample size (n) = N / (1+N[e]^2) n= sample size N=population size e=level of precision

Question 26

Q: we have 1000 milk boxes each box contains 6 milk bottles, calculate sample size for 5% accuracy?

Answer 26

(n) = N / (1+N(e)^2)) n= 6000 / ( 1+6000[0.05]^2 )

Question 27

sampling plans is classified into...

Answer 27

1. probability sampling plans | 2. non probability sampling plans

Question 28

probability sampling plans are classified into... (5)

Answer 28

1. simple random sampling 2. stratified 3. cluster 4. composite 5. systematic

Question 29

non-probability sampling plans are classified into... (5)

Answer 29

1. judgement sampling 2. convenience 3. restricted 4. quoata

Question 30

what is random sampling?

Answer 30

- each element of population has an equal chance of being included in the samples - number of units in the population needs to be known - uses a random selection process

Question 31

advantages of random sampling?

Answer 31

1. easy to conduct 2. high probability of achieving a representative sample 3. meets assumptions of many statistical procedure

Question 32

disadvantages of random sampling?

Answer 32

identification of all units of the population can be difficult

Question 33

what is stratified sampling? example?

Answer 33

- involves dividing the population into homogeneous subgroups (strata) - selecting a simple random sample or another sampling from each stratum example: eggs are divided into strata: small, medium, large and extra large

Question 34

advantages of stratified sampling?

Answer 34

- homogenous data within each stratum than in the population - cost is lower - small variances for sample size (higher statistical efficiency)

Question 35

disadvantages of stratified sampling?

Answer 35

- classification error | - prior knowledge of composition and distribution of population

Question 36

what is cluster sampling?

Answer 36

- population is divided into clusters similar to each other | - only some randomly selected clusters are sampled

Question 37

advantages of cluster sampling disadvantages

Answer 37

adv: less costly than simple or stratified dis: higher sampling error

Question 38

what is composite sampling

Answer 38

- used to obtain samples from bagged products (ie flour, seeds) - small portions are taken from different locations, bags or containers and combines in a simple sample

Question 39

what is systematic sampling?

Answer 39

1. first unit is selected at random start from first k population units. 2. units are taken every nth unit (sample interval). 3. randomly select number j between 1 and k 4. the required systematic random sample then comprises units numbered as by: j, j+k, j+2k....j + (n-1)k N population: units numbered serially from 1 to N sample size n = drawn from N k = sampling interval k = N/n

Question 40

advantages of systematic sampling?

Answer 40

easy to perform less subject to error provides greater info per unit cost

Question 41

what is probability sampling

Answer 41

selection of a sample from a population based on chance probability of inclusion and sampling errors are known

Question 42

what is the equation for calculating sample size according to precision analysis?

Answer 42

n = [ ((z) * (SD)) / (y * x) ]^2 ``` n= sample size z=z value according to level of confidence SD=standard deviation Y = accuracy x = population mean ```