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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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Testing for Differences Between Means with Small Sample Sizes and Unknown Sigma

This section addresses the situation where the population standard deviation, σ, is not known and the sample sizes are small. If one or both of our sample sizes is less than 30, the population needs to be normally distributed to use any of the following techniques. We made the same assumption for small sample sizes back in Chapters 14 and 16.
 
The sampling distribution for the difference between sample means for this scenario follows the Student’s t-distribution. Also for small sample sizes, the equation for the standard error of the difference between two means, σx1-x2 , depends on whether or not the standard deviations (or the variances) of the two populations ...

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