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# lect17 - The One-Sample t Test The Two-Sample t Test...

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The One-Sample t Test The Two-Sample t Test Outline The One-Sample t Test One-Sided Test Two-Sided Test The Two-Sample t Test 1 / 14 ISOM 2500 Lect 17: One-Sample t Test; Two-Sample t Test

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The One-Sample t Test The Two-Sample t Test One-Sided Test Two-Sided Test t - Statistc Continue our discussion about the Denver rental properties case. H 0 : μ \$ 500 versus H a : μ > \$ 500 The test statistic for testing H 0 here is t = ¯ x - μ 0 se x ) = ¯ x - μ 0 s / n , which is called a t statistic or a t ratio . The t statistic counts the number of standard errors between the observed statistic ¯ x and the hypothesized population parameter ( μ 0 ) . Intuition: a large t statistic in the direction of H a implies that the data are implausible if the null hypothesis were true. We interpret such a large t statistic as evidence against H 0 . 2 / 14 ISOM 2500 Lect 17: One-Sample t Test; Two-Sample t Test
The One-Sample t Test The Two-Sample t Test One-Sided Test Two-Sided Test Example: Testing the rental cost hypothesis H 0 : μ \$ 500 vs. H a : μ > \$ 500. The firm obtained rents for a sample of size 45, the average rent was \$647 with sample standard deviation \$ 299. The estimate of the unknown average rental μ is the sample mean ¯ x = \$647, differing from \$ 500 in the direction specified by the alternative hypothesis, (it’s bigger than μ 0 ). In units of standard errors, how far is ¯ x = \$647 from the hypothesized value μ 0 = 500? t = = = 3 . 3 ( with 44 degrees of freedom ) Inputting the observations into JMP 1 , we obtain the following results: 1 For the data in DenverRent.JMP , apply Analyze > Distribution to the column Rent , select Test Mean after clicking on the title bar, and enter 500 for the Hypothesized Mean to obtain this output. 3 / 14 ISOM 2500 Lect 17: One-Sample t Test; Two-Sample t Test

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The One-Sample t Test The Two-Sample t Test One-Sided Test Two-Sided Test The p -Value Key issue: How large should t be in order to convince us to reject H 0 ? To answer this question in our example, JMP provides the quantity: Prob > t = 0 . 0009 by which is meant that If in fact H 0 : μ \$ 500 were true, the probability of observing a t more extreme (in this example, bigger) than 3.31 is 0.0009.
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