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Jun.13 2008 Yoshioka

Statistic Seminar, Chapter.7 TESTING THE SIGNIFICANCE OF A SINGLE MEAN -The Single-Sample z and t tests-. Jun.13 2008 Yoshioka. Chapter 7. In this chapter, we deal with case I research. (cf. pp.126). Case I. Case II. z score. = the mean of the sample. = the hypothesized mean.

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Jun.13 2008 Yoshioka

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  1. Statistic Seminar,Chapter.7TESTING THE SIGNIFICANCE OF A SINGLE MEAN-The Single-Sample z and t tests- Jun.13 2008 Yoshioka

  2. Chapter 7 • In this chapter, we deal with case I research. (cf. pp.126) Case I Case II

  3. z score = the mean of the sample = the hypothesized mean = the standard deviation of the population

  4. z score (reminder) e.g. For alpha levels .05 68% Normal distribution 95% z -3.0 -2.0 -1.0 0 +1.0 +2.0 +3.0

  5. z statistics = the mean of the sample = the hypothesized mean = the standard error of the mean

  6. The sampling distribution Due to sampling error?? Hypothesized μ True μ 100 104 105 Sample

  7. The acceptance and rejection regions e.g. For alpha levels .05 (Critical region) 95% 2.5% 2.5% z -1.96 0 +1.96 Reject H0 Accept H0 Reject H0

  8. t statistics (Formula 7.2 pp.154) The mean of the sample The hypothesized mean The sample standard deviation Sample size

  9. Type I and Type II Errors True state of affairs H0 is true H0 is false Type II Error Correct Retain H0 Your Decision Type I Error Correct Reject H0

  10. Degree of Freedom • e.g. You can 4 numbers whatever you like. note the mean oh them should be 10. a, b, c, 10-(a+b+c)

  11. Standard Deviation Sample SD Population SD

  12. Example • Each Okadaken member takes 20 minutes to eat lunch on average. According 2weeks of investigation, Ikeuchi takes 22 minutes to eat lunch on average. Standard deviation of him was 2 minutes. • Compared to other members, is Ikeuchi a slow eater or not? note: this is an imaginary story.

  13. Solution • Identify the null and alternative hypotheses H0 : μ＝ 20 H1 : μ≠ 20 • Set alpha as .05

  14. Solution • Compute tobt using formula

  15. Solution • Find the critical value for and • The critical value is 2.262. • Compare the tobt of 3.16 to the critical value of 2.262. tobt is larger than the critical value, so H0 is rejected. • So Ikeuchi is ….

  16. Thank you for your attention!

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