sampling

Question 1

what is a sampling unit?

Answer 1

each individual thing in the population that can be sampled

Question 2

what is a population?

Answer 2

the whole set of items that are of interest

Question 3

what is a sample?

Answer 3

some subset of the population intended to represent the whole population

Question 4

what is a sampling frame?

Answer 4

a list of the sampling unit of a population

Question 5

what is a census?

Answer 5

data collected from an entire population

Question 6

name an advantage of a census?

Answer 6

should give completely accurate result

Question 7

name 3 disadvantages of a census?

Answer 7

.time consuming and expensive.
.large amounts of data to process
.can not be used when testing invovles destruction

Question 8

name 2 advantages of a sample?

Answer 8

less expensive and time consuming
less amount of data needs processing

Question 9

name 2 disadvantages of a sample?

Answer 9

.data may not be accurate
.data may not be large enough to represent sub-groups

Question 10

Example: A supermarket wants to test a delivery of avocados for ripeness by cutting them in half.
.Suggest a reason why the supermarket should not test all the avocados in the delivery.
.The supermarket tests a sample of 5 avocados and finds that 4 of them are ripe. They estimate that 80% of the avocados in the deliver are ripe. Suggest one way that the supermarket could improve their estimate.

Answer 10

1. testing all the avocadoes detroys them so they can not be sold
2. by testing a larger sample the supermarket can improve the accuracy of the estimation

Question 11

what is simple random sampling?

Answer 11

when every item in the population has an equal chance of being selected

Question 12

how is simple random sampling carried out?

Answer 12

• number each item in a sampling frame
• select n random numbers, where n is the sample size, using a random number generator or random number table
• select the items from the sampling frame that correspond to those random numbers

Question 13

what is systematic sampling-

Answer 13

whereby a sample is chosen by slecting items at regular intervals from an ordered list

Question 14

how is a systematic sample carried out?

Answer 14

.number every item . . Take every kth elements where:

k=(pop size (N))/(samp size (n) )

starting at random item between 1 and k.

Question 15

what is quota sampling?

Answer 15

the population is divided into strata. number of items in each stratum is set to try to reflect its proportion within the population (an interviwer selects the items so this process is not random)

Question 16

what is opportunity sampling?

Answer 16

invloves sampling items of the population which are conveniently placed to take part in the survey and fit the required criteria

Question 17

what is stratisfied sampling?

Answer 17

the population is divided into strata, the number of items in each startum is set to reflect its propotion within the population. the itms within each stratum are selected at random

Question 18

what is strata?

Answer 18

groups in which the population can be divided that are mutually exclusive (no item can be placed in two are more groups). for example religion, age, gender etc

Question 19

name two advantages of simple rnadom sample?

Answer 19

• simple and cheap
• minimises sample bias

Question 20

name 2 disadvatages of simple rnadom sample?

Answer 20

• a sampling frame required
• not suitable for large populations

Question 21

There are 64 girls and 56 boys in a school. Explain briefly how you could take a random sample of 15 pupils using a simple random sample. (3)

Answer 21

• allocate a number 1 to 120 to each pupil.
• use a random number table or generator to select 15 different numbers, between 1 and 120
• the pupils coresponding to these numbers become the same.

Question 22

A school has 15 classes and a sixth form. In each class there are 30 students. In the sixth form there are 150 students. There are equal numbers of boys and girls in each class. There are equal numbers of boys and girls in the sixth form. The head teacher wishes to obtain the opinions of the students about school uniforms. Explain how the head teacher would take a stratified sample of size 40.

Answer 22

.total in school equal (15*30) +150=600

.random sample of 30/600*40=2 from each class room

.random sample of 150/600*40=10 from each sixth form

.label the boys in each class 1 - 15 and the girls 1-15

.use random number to select 1 boy and 1 girl

label the boys in the sixth form from 1 -75, use a random number generator to select 5 differnt boys and 5 differnt girls.

Question 23

A telephone directory contains 50 000 names. A researcher wishes to select a systematic sample of 100 names from the directory. Explain in detail how the researcher should obtain such a sample. (2)

Answer 23

• randomly selcet a number between 1 and 500
• then select every 500th person