stats math

Popular wisdom is that eating pre-sweetened cereal tends to increase the
number of dental caries (cavities) in children. A sample of children was
(with parental consent) entered into a study and followed for several years.
Each child was classified as a sweetened-cereal lover or a non-sweetened
cereal lover. At the end of the study, the amount of tooth damage was
measured. Here is the summary data:
Group n mean std. dev
Sugar Bombed 10 6.41 5.0
No sugar 15 5.20 15.0
An approximate 95% confidence interval for the difference in the mean
tooth damage is:
ANS.

Degrees of Freedom
v=18.26

(6.41 − 5.20) ± 2.26(Sqrt.(25/10 + 225/15

i want to know where and how the 2.26 came from. I see this from the 2-tail .05 and df=9.

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  1. (6.41 − 5.20) ± 2.26(Sqrt.(25/10 + 225/15))

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  2. For 95% confidence interval, t with 9 df = ± 2.26.

    Look on table for t probabilities.

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