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Inferential Statistics-Two sample tests

Changing the temperature in a foundry process to see if the mean number of defects decreases.

Two different manufacturing processes to compare variance of finished product in each batch.

Are 10th standard girls taller than 10th standard boys in India.

Single set of data versus two sets of data

Think of it as dealing with two variables for the first time   

Using the rubric for this examples:
 - Have a null and alternate hypothesis; H0:μ0 = μ1 and Halt:μ1 ≠ μ2
 

 - Do some basic calculation / 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 distribution of various variable), then the 'test statistic' should be no different than a single random draw from a specific probability distribution. This is the Z-distribution of N(0,12)
 

 - Test the probability that the "test statistic" you calculated belongs to this theoretical distribution. This is the p-value !; Use Z-tables, Excel, MatLab or R
 

- Low enough p-value is grounds for rejecting the null hypothesis 




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