GES 255

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GES 255

• Engineering Statistics I

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Material

• Chapter 7 Statistical Intervals Based on a
  Single Sample.
• Section 7.3 Intervals Based on a Normal
  Population Distribution.

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t Distribution

• Parameter is degrees of freedom, denoted by df or
  ?.
• ? n 1, where n is the sample size.
• Properties of t Distributions and Figure 7.6,
  p.300 (transparency).
• Notation for t critical value ta,?.
• Figure 7.7, p.301 (transparency).

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Example

• Determine t0.05,15 and the percentile for
• t 3.610 when ? 18.
• Appendix Tables A.5 and A.8.
• Excel Insert / Function / Statistical / TDIST
  or TINV.
• Minitab Calc / Probability Distributions / t
  (Cumulative probability or Inverse cumulative
  probability).

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A Confidence Intervalfor ?, ? Unknown, n Small

• Assumptions The population is Normally
  distributed, ? is unknown, and n is small (n
  40).
• The rv
• has a t distribution with ? (n - 1) degrees of
  freedom (df).

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A Confidence Intervalfor ?, ? Unknown, n Small

• This means that the following holds
• We use the part in parentheses to derive the
  100(1 - ?) CI.

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A Confidence Intervalfor ?, ? Unknown, n Small

• A 100(1 - ?) CI for the mean ? of a
• Normal population when the value of ? is
• unknown and n is small

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Example

• Example 7.11, p.302.
• Transparency problem statement.
• EX14 Sec.7.3 (Minitab).
• Normal probability plot (NPP).
• Two steps.
• 1. Determine the 95 CI.
• 2. Interpret the CI within the context of the
  problem.

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Example (continued)

• Minitab.
• Need sample data.
• Stat / Basic Statistics / Display Descriptive
  Statistics
• Stat / Basic Statistics / 1-Sample t

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The End!

• That is it for
• Section 7.3 Intervals Based on
• a Normal Population Distribution