# APPENDIX FMore on Inference Tools

To understand God’s thoughts, we must study statistics, for these are the measure of His purpose.

—Florence Nightingale

Chapter 9 presented inference tools, focusing on confidence intervals and hypothesis tests. Formulas that illustrated key concepts were included in the text; in other cases, no formula was given. This appendix provides one concise reference for the most common confidence intervals and hypothesis tests by listing the hypotheses being tested as well as the appropriate formulas and “degrees of freedom.” Of course, you typically can perform all these tests using statistical software, such as JMP. For more information on inference tools, see Ledolter and Hogg1 and Walpole, Myers, Myers, and Ye.2

As can be seen in Table F.1, the tests of averages involve the t-distribution. This is because we are estimating the population standard deviation σ from the sample standard deviation s. Using a sample estimate adds additional uncertainty, or variation, which is accounted for in the t-distribution. If we knew what σ was, we would utilize the z-distribution. Using 95% confidence, the appropriate z-value is 1.96. Note that t.025 is the appropriate t-value for 95% confidence. The 0.025 means that the area above this value in the t-distribution is 0.025. There is another 0.025 below –t.025, giving a total of 0.05, for 95% confidence. For cases where we have a large sample size, say 30 or greater, we can ignore the uncertainty in s and utilize ...

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