S2

Question 1

What is a population?

Answer 1

A collection of individual people or items

Question 2

What is a census?

Answer 2

A survey of an entire population

Question 3

Give two advantages of taking a census

Answer 3

• It is unbiased

* It gives an accurate answers

Question 4

Give three disadvantages of taking a census

Answer 4

• It takes a long time to do
• It is costly
• It is often difficult to ensure that the whole population is surveyed

Question 5

What is sampling?

Answer 5

The process of only surveying a subset of an entire population

Question 6

What is a sampling unit?

Answer 6

An individual member of a sample

Question 7

What is a sampling frame?

Answer 7

A list from which a sample is drawn

Question 8

Give three advantages of sampling

Answer 8

• It is cheaper than taking a census
• It is quicker than taking a census
• It is advantageous where the testing of items results in their destruction, i.e. testing the lifetime of light bulbs

Question 9

Give two disadvantages of sampling

Answer 9

• Different samples may vary greatly

* The sample may be selected with bias

Question 10

What is a simple random sample?

Answer 10

A sample taken such that every possible sample of size n has an equal chance of being selected

Question 11

What is a statistic?

Answer 11

A quantity calculated solely from the observations in a sample

Question 12

What is a sampling distribution?

Answer 12

How the various possible values of a statistic are distributed

Question 13

What is a hypothesis?

Answer 13

A statement made about the value of a population parameter that is to be tested by collecting evidence in the form of a sample

Question 14

What is the test statistic?

Answer 14

A statistic formed from evidence from a sample in a hypothesis test

Question 15

What is the null hypothesis?

Answer 15

The hypothesis that there is no relationship between two variables, and that is assumed to be correct unless proved otherwise

Question 16

What is the critical region?

Answer 16

The range of values that are so unlikely that they would lead to the rejection of the null hypothesis

Question 17

What are the critical values?

Answer 17

The values on the boundary of the critical region

Question 18

How is the level of significance notated?

Answer 18

α

Question 19

When and how can a random variable X∼B(n,p) be approximated by a normal distribution?

Answer 19

When n is large and p is close to 0.5, then X≈∼N(np,np(1-p))

Question 20

When and how can a random variable X∼Po(λ) be approximated by a normal distribution?

Answer 20

When λ is large, then X≈∼N(λ,λ)

Question 21

What is a continuous uniform distribution?

Answer 21

A distribution in which every interval of equal width within the range of the parameters is equally likely

Question 22

How is a continuous uniform distribution notated?

Answer 22

X∼U[a,b]

Question 23

What is the probability density function of a random variable X∼U(a,b)

Answer 23

f(x)={1/(b-a) for a≤x≤b, 0 otherwise}

Question 24

For a random variable X∼U(a,b), how can E(X) be calculated?

Answer 24

(a+b)/2

Question 25

For a random variable X∼U(a,b), how can Var(X) be calculated?

Answer 25

(b-a)²/12

Question 26

For a continuous random variable with probability density function f, how can P(a≤x≤b) be calculated?

Answer 26

∫f(x) dx, a to b

Question 27

For a continuous random variable with probability density function f, what is ∫f(x) dx, -∞ to ∞ equal to?

Answer 27

1

Question 28

What is the relationship between a continuous random variable's cumulative distribution function F, and its probability density function f?

Answer 28

F(x)=∫f(t) dt, -∞ to x

Question 29

For a continuous random variable with probability density function f, how can E(X) be calculated?

Answer 29

∫xf(x) dx, -∞ to ∞

Question 30

For a continuous random variable with probability density function f, how can Var(X) be calculated?

Answer 30

(∫x²f(x) dx, -∞ to ∞) - E(X)²

Question 31

How can the mode of a continuous random variable with probability density function f be calculated?

Answer 31

It is the global maximum of f

Question 32

How can the lower/upper quartile/median of a continuous random variable be calculated?

Answer 32

It is the value x such that F(x)=0.25/0.5/0.75

Question 33

For a random variable X∼Po(λ), how can P(X=x) be calculated?

Answer 33

e^(-λ).λˣ/x!

Question 34

What conditions are required for a Poisson distribution?

Answer 34

* The events occur singly in space or time * The events are independent * The events occur at a constant rate, such that the mean number of occurrences in the interval is proportional to the length of the interval

Question 35

When and how can a random variable X∼B(n,p) be approximated by a Poisson distribution?

Answer 35

When n is large and p is small, then X≈∼Po(np)

Question 36

What is the mean and variance of a Poisson distribution?

Answer 36

λ

Question 37

How many ways can n objects be arranged?

Answer 37

n!

Question 38

What does the notation ⁿCₐ mean?

Answer 38

n!/(a!(n-a)!)

Question 39

How many ways can n objects be arranged when there's a of one type and n-a of another?

Answer 39

ⁿCₐ

Question 40

What conditions are required for a binomial distribution?

Answer 40

* A fixed number of trials * Each trial can only result in a success or a failure * The trials are independent * The probability of success is constant for each trial

Question 41

For a random variable X∼B(n,p), how can P(X=x) be calculated?

Answer 41

ⁿCₓ*pˣ*(1-p)ⁿ⁻ˣ