All S2

Question 1

What are the conditions for using a binomial distribution?

Answer 1

• A fixed number of trials, n.
• Each trial should be success or failure.
• The trials are independent
• The probability of success, p, at each trial is constant.

Question 2

What is the definition of a population?

Answer 2

A population is a collection of individual items.

Question 3

What is a sample?

Answer 3

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

Question 4

What is a finite population?

Answer 4

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

Question 5

What is an infinite population?

Answer 5

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

Question 6

What is a sampling unit?

Answer 6

A sampling unit is an individual member of a population.

Question 7

What is a sampling frame?

Answer 7

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

Question 8

What is a statistic?

Answer 8

A statistic is a quantity calculated solely from the observations in a sample.
A random variable; function of known observations (from a population)
A random variable) that is a function of the sample which contains no unknown quantities/parameters.

Question 9

What is the sampling distribution of a statistic?

Answer 9

A statistic has a sampling distribution that is defined by giving all possible values of the statistic and the probability of each occurring.

Question 10

What is a census?

Answer 10

If information is to be obtained from all members of the population, the investigation is known as a census.

Question 11

What are the advantages of taking a census?

Answer 11

• Every single member of the population is used
• It is unbiased
• It gives an accurate answer

Question 12

What are the disadvantages of taking a census?

Answer 12

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

Question 13

What are the advantages of sampling?

Answer 13

• Sampling is generally cheaper than taking a census
• Sampling is advantageous where the testing of items results in their destruction.
• Data is generally more readily available.

Question 14

What are the disadvantages of sampling?

Answer 14

• Uncertainty about sampling in that there will be natural variation between any two samples.
• Bias can more easily occur, e.g. sample from an incomplete sampling frame.

Question 15

What is a test statistic?

Answer 15

A test statistic is the summary of the evidence that comes from a sample in a hypothesis test.

Question 16

What is a null hypothesis?

Answer 16

The null hypothesis, denoted by Ho, is the hypothesis that we assume to be correct unless proved otherwise.

Question 17

What is the alternative hypothesis?

Answer 17

The alternative hypothesis, denoted by H1, tells us about the value of the population parameter if our assumption is shown to be wrong.

Question 18

What is a critical region?

Answer 18

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

Question 19

What is a critical value?

Answer 19

The boundary value(s) of a critical region is (are) called the critical value(s).

Question 20

What is a one-tailed test?

Answer 20

A one-tailed test looks either for an increase or for a decrease in a parameter, and has a single critical value.

Question 21

What is a two-tailed test?

Answer 21

A two-tailed test looks for both an increase and a decrease in a parameter, and has two critical values.

Question 22

What is the actual significance level of a test?

Answer 22

The probability of rejecting H0.

Question 23

What are the conditions for using a poisson distribution?

Answer 23

• Event occurs singly in time

- Events are independent or occur randomly - Event occurs at a constant rate

Question 24

Approximate X-Po($) to Normal distribution.

Answer 24

Y - N ( $ , ( sqr ($) ) ^2 )

Question 25

Approximate X-B(n,p) to Normal distribution.

Answer 25

Y - N ( np , sqr ( np x (1-p) )

Question 26

Approximate X-B(n,p) to Poisson distribution.

Answer 26

Y - Po ( np )

Question 27

How do you find the median of a continuous random variable?

Answer 27

F(m) = 0.5

Question 28

How do you find the mode of a continuous random variable?

Answer 28

The mode is the x value at the highest point of the function..

Question 29

Continuity correction.

P(X=n)

Answer 29

P ( n-0.5 < X < n+0.5 )

Question 30

Continuity correction.

P(X<=n)

Answer 30

P ( X < n+0.5 )

Question 31

Continuity correction.

P(X>n)

Answer 31

P ( X > n+0.5 )

Question 32

Continuity correction.

P(X

Answer 32

P ( X < n-0.5 )

Question 33

Continuity correction.

P(X>=n)

Answer 33

P ( X > n-0.5 )

Question 34

What is a hypothesis test?

Answer 34

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

Question 35

Positive skew?

Answer 35

mode < median < mean

Question 36

Negative skew?

Answer 36

mode > median > mean

Question 37

What are the conditions for approximating binomial to normal?

Answer 37

• n is large

- p is close to 0.5

Question 38

What are the conditions for approximating poisson to normal?

Answer 38

Lamda is large

Question 39

What are the conditions for approximating binomial to poisson?

Answer 39

• n is large

- p is small (approx<0.2)