S2 Definitions + Conditions

Question 1

Actual Significance Level

Answer 1

The actual significance level of a test is the probability of a value falling in the critical region and hence incorrectly rejecting H0 when it is in fact true.

Question 2

Census

Answer 2

An investigation in which every member of the population is investigated

Question 3

Critical Region

Answer 3

The critical region is the range of values of a test statistic that would lead you to reject the null hypothesis, H0

Question 4

Hypothesis Test

Answer 4

A hypothesis test is a mathematical procedure to examine a value of a population parameter proposed by the null hypothesis, H0, compared to the alternative hypothesis H1.

Question 5

Population

Answer 5

A population is a collection of all items

Question 6

Sampling Distribution (of a Statistic)

Answer 6

The probability distribution of the statistic from all possible samples.

This is the set of all possible values of the statistic together with their individual probabilities;

This is sometimes better described by giving the relevant probability density function

Question 7

Sampling Frame

Answer 7

A list of all sampling units

Question 8

Sampling Units

Answer 8

An individual member of a population which could be included in a sample

Question 9

Statistic

Answer 9

A random variable that is a function of the sample which is calculated solely from the observations in the sample and contains no unknown parameters.

Question 10

Finite Population

Answer 10

A population in which each individual can be given a number

Question 11

Infinite Population

Answer 11

A population in which it is impossible to number each member

Question 12

Sample

Answer 12

A selection of individual members or items from a population.

A selection of sampling units from the sampling frame.

Question 13

Simple Random Sample

Answer 13

A sample taken so that every possible sampling unit has an equal chance of being selected.

Question 14

Sample Survey

Answer 14

An investigation using a sample.

Question 15

Advantages of taking a census

Answer 15

> Every member of the population is used.

> It is unbiased.

> It gives an accurate answer.

Question 16

Disadvantages of taking a census

Answer 16

> It takes a long time

> It is costly

> It is often difficult to ensure that the whole population is surveyed

Question 17

Advantages of sampling

Answer 17

> Sample will be representative if the population large and well mixed.

> Usually cheaper than taking a census

> Essential if testing results in destruction of sampling units (e.g. life of a light bulb, etc.).

> Data usually more readily available than in a census.

Question 18

Disadvantages of sampling

Answer 18

> Uncertainty, due to the natural variation – two samples are unlikely to give the same result.

> Uncertainty due to bias which occurs when taking a sample which prevents it from being truly representative of the population from which it is taken.

> Bias can occur if you sample from an incomplete sampling frame, or if you get responses only from people that have a particular interest in the topic being studied.

> Bias can occur if the person taking the sample allows their personal feelings to influence their choice.

Note: Bias can be removed by increasing the size of the sample.

Question 19

Null Hypothesis, H0

Answer 19

The hypothesis that we assume to be correct unless proved otherwise.

Question 20

Alternative Hypothesis, H1

Answer 20

The conclusion that should be made if H0 is rejected.

Question 21

Test Statistic

Answer 21

This is the statistic (calculated from the sample) which is tested as the last part of the significance test.

In a statistical hypothesis test the evidence comes from a sample which is summarized in the form of a statistic called the test statistic.

Question 22

Conditions for modelling with a binomial distribution

Answer 22

> A fixed number of trails

> Each trial should be a success or a failure

> The trails are independent

> The probability of success at each trial is constant

Question 23

Conditions for modelling with a Poisson distribution

Answer 23

> Events occur singly in the space or time

> Events occur independently of each other

> Events occur at a constant rate

> Events occur randomly

Question 24

Conditions for approximating binomial with Poisson

Answer 24

If X - B(n, p) and

> n is large

> p is small

> np < or = 10

Question 25

Conditions for approximating binomial with normal

Answer 25

If X - B(n, p) and

> n is large

> p is close to 0.5

And/Or

> np > 10

Note: Add Comtinuity Correction and Standerdise to get value of Z.

Question 26

Conditions for approximating Poisson with normal

Answer 26

If X - Po(Lmda.) and

> Lmda. > 10