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Hypothesis testing for means - t scores

I don't understand the formulas and rationales for the attached. I also don't have the correct version of excel to use the tool pack I need so I am doing everything manually. I am doing the work on my own but want to make sure it is somewhat correct prior to turning in. Any help would be appreciated. Thank you.

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Solution Summary

The solution gives detailed step on conducting hypothesis testing for population means of either one sample or two independent samples. All formula and calculations are shown and explained.