All S2 Flashcards
What are the conditions for using a binomial distribution?
- 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.
What is the definition of a population?
A population is a collection of individual items.
What is a sample?
A sample is a selection of individual members or items from a population.
What is a finite population?
A finite population is one in which each individual members can be given a number.
What is an infinite population?
An infinite population os one in which it is impossible to number each member.
What is a sampling unit?
A sampling unit is an individual member of a population.
What is a sampling frame?
A sampling frame is a list of sampling units used in practice to represent a population.
What is a statistic?
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.
What is the sampling distribution of a statistic?
A statistic has a sampling distribution that is defined by giving all possible values of the statistic and the probability of each occurring.
What is a census?
If information is to be obtained from all members of the population, the investigation is known as a census.
What are the advantages of taking a census?
- Every single member of the population is used
- It is unbiased
- It gives an accurate answer
What are the disadvantages of taking a census?
- It takes a long time to do
- It is costly
- It is often difficult to ensure that the whole population is surveyed
What are the advantages of sampling?
- 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.
What are the disadvantages of sampling?
- 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.
What is a test statistic?
A test statistic is the summary of the evidence that comes from a sample in a hypothesis test.
What is a null hypothesis?
The null hypothesis, denoted by Ho, is the hypothesis that we assume to be correct unless proved otherwise.
What is the alternative hypothesis?
The alternative hypothesis, denoted by H1, tells us about the value of the population parameter if our assumption is shown to be wrong.
What is a critical region?
The critical region is the range of values of a test statistic that would lead you to reject H0
What is a critical value?
The boundary value(s) of a critical region is (are) called the critical value(s).
What is a one-tailed test?
A one-tailed test looks either for an increase or for a decrease in a parameter, and has a single critical value.
What is a two-tailed test?
A two-tailed test looks for both an increase and a decrease in a parameter, and has two critical values.
What is the actual significance level of a test?
The probability of rejecting H0.
What are the conditions for using a poisson distribution?
- Event occurs singly in time
- Events are independent or occur randomly - Event occurs at a constant rate
Approximate X-Po($) to Normal distribution.
Y - N ( $ , ( sqr ($) ) ^2 )
Approximate X-B(n,p) to Normal distribution.
Y - N ( np , sqr ( np x (1-p) )
Approximate X-B(n,p) to Poisson distribution.
Y - Po ( np )
How do you find the median of a continuous random variable?
F(m) = 0.5
How do you find the mode of a continuous random variable?
The mode is the x value at the highest point of the function..
Continuity correction.
P(X=n)
P ( n-0.5 < X < n+0.5 )
Continuity correction.
P(X<=n)
P ( X < n+0.5 )
Continuity correction.
P(X>n)
P ( X > n+0.5 )
Continuity correction.
P(X
P ( X < n-0.5 )
Continuity correction.
P(X>=n)
P ( X > n-0.5 )
What is a hypothesis test?
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.
Positive skew?
mode < median < mean
Negative skew?
mode > median > mean
What are the conditions for approximating binomial to normal?
- n is large
- p is close to 0.5
What are the conditions for approximating poisson to normal?
Lamda is large
What are the conditions for approximating binomial to poisson?
- n is large
- p is small (approx<0.2)
