Populations and Samples

Question 1

What is a population?

Answer 1

A population is a collection of individual items

Question 2

What is a finite population?

Answer 2

A finite population is one in which each individual member can be given a number

Question 3

What is an infinite population?

Answer 3

An infinite population is one in which it is impossible to number each member

Question 4

What is a countably infinite population?

Answer 4

A population may be of countably infinite size if we know that the population could be infinite but in practice we can count the number of individual members of it

Question 5

What is a census?

Answer 5

If information can be obtained from all members of the population, the investigation is called a census

Question 6

What are the advantages and disadvantages of taking a census?(3,3)

Answer 6

Advantages:

1. Every single member of the population is used
2. It is unbiased
3. It gives an accurate answer

Disadvantages:

1. It takes a long time to do
2. It is costly
3. It is often difficult to ensure that the whole population is surveyed

Question 7

What is a sample?

Answer 7

A sample is a selection of individual members or items from a population

Question 8

What is a sampling unit?

Answer 8

A sampling unit is an individual member of a population

Question 9

What is a sampling frame?

Answer 9

A sampling frame is a list of sampling units used in practice to represent a population

Question 10

What is a sample survey?

Answer 10

An investigation using a sample is called a sample survey

Question 11

What are the advantages and disadvantages of sampling?(4,2)

Answer 11

Advantages:

1. If a population is large and well mixed a sample will be representative of the whole population
2. Sampling is generally cheaper than taking a census
3. Sampling is advantageous where the testing of items results in their destruction
4. When using a sample rather than a census, data is generally more readily available

Disadvantages:

1. There is an uncertainty about sampling in that there will be natural variation between any two samples due to the natural variation between the individual units that make up the samples
2. Another source of uncertainty is called bias. Bias is anything which occurs when taking a ample which prevents it from being truly representative of the population from which it is taken. It can occur from an incomplete sampling frame

Question 12

What is a simple random sample?

Answer 12

A simple random sample, of size n, is one taken so that every possible sample of size n has an equal chance of being selected

A simple random sample of size n consists of the observations X1, X2, …, Xn from a population where the Xi:

• are independent random variables
• have the same distribution as the population

Question 13

What is a population parameter?

Answer 13

A population parameter is a characteristic of a population which is measurable ie population mean, µ, population variance σ² (numerical)

Question 14

What is a statistic?

Answer 14

A statistic is a quantity calculated solely from the observations in a sample. It does not involve ant unknown parameters ie a statistic is a numerical property of a sample ie a sample mean, xbar

Question 15

What is a sampling distribution?

Answer 15

The sampling distribution of a statistic gives all the values of a statistic and the probability that each would happen by chance alone, ie it is a distribution of all sample statistics from a population