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Estimation of a Population Mean: σ Unknown

Estimation of a Population Mean: σ Unknown. Section 8.4. Conditions:. The t Distribution. Bell-shaped curve like normal distribution. More area in tails. Becomes more like the normal curve as n increases. Degrees of Freedom = n-1. t distribution. Using t Distribution Table. Using t*.

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Estimation of a Population Mean: σ Unknown

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  1. Estimation of a Population Mean: σ Unknown Section 8.4

  2. Conditions:

  3. The t Distribution • Bell-shaped curve like normal distribution. • More area in tails. • Becomes more like the normal curve as n increases. • Degrees of Freedom = n-1.

  4. t distribution

  5. Using t Distribution Table

  6. Using t* • t* gives the value of t with a certain area to its right at a certain number of degrees of freedom.

  7. Confidence Interval for the t Distribution • Conditions must be met. • We use s (standard deviation of the sample) in place of σ (unknown). • Confidence interval: x ± t*s/√n Margin of Error (ME or E)

  8. Example: Male Cholesterol Levels • Mean cholesterol level for a sample of 25 men = 186, with a st dev of 12. Assume all adult males have a normal distribution of cholesterol levels. Construct a 95% confidence interval for the average cholesterol levels of adult males. • State facts, draw: • Calculate Interval: • Summarize results: (181.05, 190.95)

  9. Example: Book Expenses • A sample of 64 adults spent on average $1450 per year on books with a standard deviation of $300. Determine a 99% confidence interval for the average amount spent on books per year for all adults. • State facts, draw: • Calculate Interval: • Summarize results: ($1350.40, $1549.60)

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