Chem-3000-Lab-Manual-Fall-2009__tTest

# Chem-3000-Lab-Manual-Fall-2009__tTest - A PPENDIX A...

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A PPENDIX A Student’s t -test A.1 General t test The steps in the t -test are 1. Write down the mean μ that I expect to see. 2. Take n data points. Compute the mean ¯ x n and the standard deviation s n of the data. 3. Formulate a primary and a backup hypothesis, as follows: Null hypothesis : μ and x n are the same. Alternate hypothesis : μ and x n are not the same. 4. Compute the experimental, or measured, t value t exp = | ¯ x n - μ s n | n (A.1) 5. Compute the degrees of freedom ν in the data ν = n - 1 (A.2) 6. Decide on a confidence level and compute α = 1 - confidence level 100% (A.3) For a confidence level of 95%, α = 0 . 05 . 7. Take the ν and α and look up the critical value t crit in a t Table (Fig. A.1 ). 8. Test the hypotheses: t > t crit : reject the null hypothesis; accept the alternate hypothesis; conclude that μ and x n are not the same. t < t crit : accept the null hypothesis; reject the alternate hypothesis; conclude that μ and x n are the same.

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