I have consulted two texts on how to calculate to calculate confidence intervals when N is small and the population standard deviation is unknown. There are some differences in the formulas they give and the end result varies depending on which text I follow (although not by a large amount). Text one says:
- Calculate the mean
- Calculate the standard deviation using the formula: s= √ ((∑ X(squared)/N)–X-bar)
- Calculate the standard error of the mean using the formula: s/√ N-1
- Determine the value of T from the t-table
- Obtain the margin of error by multiplying the standard error of the mean by multiplying it by the value obtained in step 4.
- Add and subtract this product from the sample mean to obtain the C.I.
Steps, 1,4,5& 6 are exactly the same in the second text. However it gives different formulas for steps 2 & 3. It says:
- Calculate the standard deviation using the formula: s= √ ((∑ X(squared) /N-1) –X-bar). The difference is that they reduce N by one.
- Calculate the standard error of the mean using the formula: s/√ N The difference is that N is not reduced by 1.
Can anyone explain why the different formulas are used and why?
Thanks. Anne S