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 7.2 Large-Sample Confidence Intervals
  for a Population Mean and Proportion.

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A Confidence Intervalfor ?, ? Unknown, n Large

• Assumptions ? is unknown and n is large (n gt
  40).
• The rv
• is approximately Normally distributed with mean
  zero and standard deviation one (CLT).

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A Confidence Intervalfor ?, ? Unknown, n Large

• 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 Large

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

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Example

• Example 7.6, p.292.
• Transparency problem statement.
• EX13 Sec.7.2 (Excel and Minitab).
• Two steps.
• 1. Determine the 95 CI.
• 2. Interpret the CI within the context of the
  problem.

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Example (continued)

• Excel.
• CONFIDENCE(?, ?, n) function.
• Minitab.
• Need sample data.
• Stat / Basic Statistics / Display Descriptive
  Statistics
• Stat / Basic Statistics / 1-Sample Z

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A Confidence Interval for p, n Large

• Assumption n is large (n 10 and n(1 -
  ) 10).
• The rv
• is approximately Normally distributed with mean
  zero and standard deviation one.

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A Confidence Interval for p, n Large

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

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A Confidence Interval for p, n Large

• An approximate 100(1 - ?) CI for the
• population proportion p when n is large

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Example

• Example 7.8, p.295.
• Transparency problem statement.
• EX13 Sec.7.2 (Minitab).
• Two steps.
• 1. Determine the 95 CI.
• 2. Interpret the CI within the context of the
  problem.
• Minitab Stat / Basic Statistics /
  1 Proportion

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One-Sided Confidence Intervals

• A large-sample upper confidence bound for ?
• A large-sample lower confidence bound for ?

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Example

• Example 7.10, p.297.
• Transparency problem statement.
• EX13 Sec.7.2 (Excel).
• Two steps.
• 1. Determine the 95 CI.
• 2. Interpret the CI within the context of the
  problem.
• Excel CONFIDENCE(?, ?, n) function.

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The End!

• That is it for Section 7.2
• Large-Sample Confidence Intervals
• for a Population Mean and Proportion