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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
The One-Sample t Test The Two-Sample t Outline The One-Sample t One-Sided Test Two-Sided Test The Two-Sample t 1 / 14 ISOM 2500 Lect 17: One-Sample t Test; Two-Sample t
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The One-Sample t Test The Two-Sample t 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
Background image of page 2
The One-Sample t Test The Two-Sample t 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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The One-Sample t Test The Two-Sample t 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.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/20/2011 for the course ACCT/MGMT 2010 taught by Professor A during the Spring '11 term at HKUST.

Page1 / 14

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online