If the answer is Yes then use Z statistics, otherwise use Student T statistics.
Each of the test statistics have their own formula which I have explained in my other blog.
Step 5: Calculate The Test StatisticsBased on the chosen test statistics in step 4, apply the formula and calculate the value.
Compare the value with the level of significance.
Step 6: State DecisionBased on the results of the calculation in step 5, whether the hypothesis analysis is accepted or rejected is stated.
These set of steps are dependent on the sample that was chosen and how good the tests were.
This implies that there is always a chance that an error was made.
For example, the tests could end up proving Null Hypothesis wrong when it is right or could end up proving Alternative Hypothesis wrong when it is right.
Types Of Errors: Type 1 And Type 2In Hypothesis Analysis, there are two types of errors:Type 1 error: Null Hypothesis was correct but the analysis proved it wrongType 2 error: Null Hypothesis was wrong but the analysis couldn’t prove that it was wrongHypothesis Analysis Explained With An ExampleLet’s assume you are an IT manager in a hedge fund.
One of your critical systems runs an overnight batch and it has slowed down significantly.
The batch now takes on average 12 hours to complete daily.
It has been notified by the support team and you are looking for alternative solutions to the current IT system.
As there is cost associated with running batches for the hypothesis, the IT management concludes that it only makes sense to replace the existing framework if the new framework ensures on average each batch job completes in less than 6 hours.
This implies that if the test concludes that a job takes longer than 6 hours then the management will not accept the new IT framework.
An external consultancy contacts you and offers you to use their framework which would ensure on average each batch job completes in 6 hours.
Before you accept it blindly, you decide to test the Hypothesis.
You get the framework installed on a test environment.
Additionally, you then decide to run a sample of jobs; some at night and some in the mornings.
TestA sample of 30 batch jobs is chosen.
Let x be time of a batch job in a sample.
Null Hypothesis: Mean of sample jobs is less or equal to 6 hoursAlternative Hypothesis: Mean of sample jobs is equal or greater than 6 hoursYou can see that your Alternative Hypothesis is one tailed as the mean of the jobs can turn out to be greater than 6 hours.
Additionally, you then attempt to run 30 batch jobs and calculate the mean and variance of your sample.
As you know the variance of your sample, you can test using Z Statistics Test.
There is always a room for errors (min.
threshold) and it is the level of significance.
You decide that the level of significance is 1% so you will only accept Null Hypothesis if the average job time falls in 1%Perform z stats calculation — it has a well known formulaState your decisionThese set of easy to follow steps can be used to articulate whether a hypothesis is correct or not.
It helps one make conscious risk averse decisions.
SummaryThe article highlighted concept of Hypothesis Analysis which is used in a number of fields including risk management, finance, stats and artificial intelligence.
Furthermore, it helps researchers gain better insight into the data.
Hope it helps.
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