Introduction :-
Making an inference about a population from a sample.
The need for an inference: One-sample and two-sample examples
One-sample situations:-
- Average Phosphate levels in Blood should =< 4.8 mg/dl
- Health department only allows 5% of the toothpastes of each brand to be out of specification (ration of fluoride, abrasives, etc.)
- New garage is inflating repair costs for accidents. Insurance fraud is suspected.
Two-sample situations
- Changing the temperature in a foundry process to see if the mean number of defects decreases.
- Two different manufacturing process to compare variance of finished product in each batch.
- Are 10th standard girls taller than 10th standard boys in India.
Sampling Distribution:-
The overarching principle:
- Have a null and alternate hypothesis
- Do some basic calculations/arithmetic on the data to create a single number called the "test statistic"
- If we assume the null hypothesis to be true (and make some assumptions about the distributions of various variables), then the 'test statistic' should be no different than a single random draw from a specific probability distribution.
- Test the probability that the "test statistic" you calculated belongs to this theoretical distribution. This is the p-value !
- Ergo : Its D | H not H | D
Inferential Statistics - Single sample tests
Inferential Statistics-Two sample tests
Making an inference about a population from a sample.
The need for an inference: One-sample and two-sample examples
One-sample situations:-
- Average Phosphate levels in Blood should =< 4.8 mg/dl
- Health department only allows 5% of the toothpastes of each brand to be out of specification (ration of fluoride, abrasives, etc.)
- New garage is inflating repair costs for accidents. Insurance fraud is suspected.
Two-sample situations
- Changing the temperature in a foundry process to see if the mean number of defects decreases.
- Two different manufacturing process to compare variance of finished product in each batch.
- Are 10th standard girls taller than 10th standard boys in India.
Sampling Distribution:-
- Have a null and alternate hypothesis
- Do some basic calculations/arithmetic on the data to create a single number called the "test statistic"
- If we assume the null hypothesis to be true (and make some assumptions about the distributions of various variables), then the 'test statistic' should be no different than a single random draw from a specific probability distribution.
- Test the probability that the "test statistic" you calculated belongs to this theoretical distribution. This is the p-value !
- Ergo : Its D | H not H | D
Inferential Statistics - Single sample tests
Inferential Statistics-Two sample tests
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