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7.1 confidence Intervals for the Mean When SD is Known

7.1 confidence Intervals for the Mean When SD is Known. -A point estimate is a specific numerical value that estimates a parameter. -The best point estimate of the population mean µ is the sample mean X. . 3 Properties of a good estimator.

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7.1 confidence Intervals for the Mean When SD is Known

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  1. 7.1 confidence Intervals for the Mean When SD is Known

  2. -A point estimate is a specific numerical value that estimates a parameter. • -The best point estimate of the population mean µ is the sample mean X.

  3. 3 Properties of a good estimator • Unbiased: the mean of estimates is equal to the parameter being estimated. • Consistent: as the sample size increases, the value of the estimator approaches the value of the parameter. • Relatively Efficient: has the smallest variance

  4. Confidence Intervals • Interval Estimate: an interval (range) used to estimate the parameter. • -may or may not contain the parameter • Ex. 20 < µ < 25

  5. Confidence Intervals • Confidence Level- probability that the interval estimate will contain the parameter • -three common levels are 90%, 95%, and 99% • Confidence Interval- specific interval estimate of a parameter • -determined by using data and specific confidence levels • -as the percent increases, so does the range of the interval.

  6. Formula for the confidence interval X = sample mean For 90% confidence interval: N = sample size σ = standard deviation 95% confidence interval: 99% confidence interval:

  7. MARGIN of error • The maximum likely difference between the point estimate and the actual value of the parameter.

  8. A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Chevrolet Aveo. A sample of 50 cars had a mean time on the dealer’s lot of 54 days. Assume the population standard deviation to be 6.0 days. Find the best point estimate of the population mean and the 95% confidence interval of the population mean.

  9. So, we can say with 95% confidence that the interval between 52.3 and 55.7 does contain the population mean.

  10. A survey of 30 emergency room patients found that the average waiting time for treatment was 174.3 minutes. • Assuming that the population standard deviation is 46.5 minutes, find the best point estimate of the population mean and the 99% confidence of the population mean.

  11. Practice problems: p. 366 • Numbers 11, 13, 14, 15, 17

  12. Determining Sample size E = margin of error N = sample size σ = standard deviation depends on confidence interval

  13. - A scientist wishes to estimate the average depth of a river. He wants to be 99% confident that the estimate is accurate within 2 feet. From a previous study, the standard deviation of the depths measured was 4.33 feet. How large a sample is required?

  14. Practice! • p. 367 numbers 21, 23, 24, 25

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