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QT-1, P20 B1, Chi Square test, How to conduct Hypothesis test, U1 A1, U1…
QT-1
P20 B1
Stochastic Problems are not characterized by
Certainty
Probability deals with
Chances
Probability of two independent events, A and B, happening together or in succession is
given as:
P(A)*P(B)
Expected value of a random variable is:
P1V1 + P2V2
P(B/A) = P(B)- when is it relevant
Statistical Independence
Chi Square test
When to use?
You want to test a hypothesis about one or more categorical variables
The sample was randomly selected from the population
There are a minimum of five observations expected in each group or combination of groups
Steps in chi square test
Create a table of the observed and expected frequencies.
Calculate the chi-square value from your observed and expected frequencies using the chi-square formula.
Find the critical chi-square value in a chi-square critical value table
Compare the chi-square value to the critical value
Decide whether to reject the null hypothesis.
How to conduct Hypothesis test
State the Hypotheses
Formulate an Analysis Plan
Analyze Sample Data
Interpret Results
Test Your Understanding
Null Hypothesis
Alternative Hypothesis
A claim that there is no effect in the population
A claim that there is an effect in the population
Limitation:
Can only be rejected but not proven
Only dichotomous
Of the two decision is made based on assumption all information is available
U1 A1
Explain the concept and types of probability
Probability is the quality or state of an event being probable, that is the extent to which
that event is likely to happen.
Computing the chance, chances, likelihood,
likeness or possibility of happening or not-happening of an event in isolation or events together
with or without conditions attached, is what study of probability helps us to probe.
Four Concepts of Probability:
the quality or state of being probable; the word ‘probable’ means, something that is supported by evidence strong enough to establish a presumption but not essentially a proof.
the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that
produce a given event to the total number of possible outcomes
a branch of mathematics concerned with the study of probabilities
a logical relation between statements such that evidence confirming one confirms the
other to some degree
U1 A2
Present the uses of probability to investment decision making in business and industry
Business application of probability
The key role of probability is to improve decision-making in the face of uncertainties. It helps decision-making objective and data-driven rather than based on instinct.
U1 A4
A
Joint Probability is the probability of two or more events happening together or insuccession. It is notated as: P(A)”B) or P(A and B) or P(AB). Joint Probability of A and B = P(AB) = P(A)*P(B), where P(AB) is the probability two events A and B happening together or in succession
Conditional Probability is probability of an event happening given that another event has happened. It is written as P(B/A) or P(X/Y) and so on. When it is written as read as P(B/A) it measures or means the Probability of event B happening, given that event A has already happened. When it is written as read as P(X/Y) it measures or means the Probability of event X happening, given that event Y has already happened. But under statistical independence, conditional probability has no relevance as the event is independent of other event or events.
Marginal Probability is also known as unconditional probability. Generally it is noted as: P(A), P(B), P(X), P(Y), and so on. Marginal Probability is the simple probability of the occurrence of an event, A, B, X, Y or others.
Probability approach
Classical-
Frequency
Subjective
Types of sampling
Probability sampling
Non probability sampling
Probability sampling
a. Simple random
b. stratified
c. cluster
d. systematic sampling
Non probable sample
a. convenience sample
b. voluntary response
c. purposive
d. snowball sampling
e. quota sampling
Probability sampling also known as random sampling
Lottery sampling - Each member of the population is assigned a number and then such number is picked at random
Poisson distribution
It gives the probability of an event happening a certain number of times (k) within a given interval of time or space.
F Test
1.F test is a statistical test that is used in hypothesis testing to check whether the variances of two populations or two samples are equal or not.
follows an f distribution
This test uses the f statistic to compare two variances by dividing them
An f test can either be one-tailed or two-tailed depending upon the parameters of the problem.
Sample Survey
A survey is an investigation into the characteristics of a given population that involves collecting data from a sample of that population and estimating their characteristics using statistical methods in a systematic manner.
Factors affecting size of sample
Population size
Cost involved
Convenience and accessibility