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Review of Inference

Review of Inference. Confidence Interval Estimates Tests of Hypotheses. Estimates of the mean, m. When s is known and X is normal or n > 30 Page 307 Problem 10.24 page 319 When s is unknown and X is normal or n > 30 Page 363 Problem 12.22 page 372. Estimates of the proportion, p.

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Review of Inference

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  1. Review of Inference Confidence Interval Estimates Tests of Hypotheses

  2. Estimates of the mean, m • When s is known and X is normal or n>30 • Page 307 • Problem 10.24 page 319 • When s is unknown and X is normal or n > 30 • Page 363 • Problem 12.22 page 372

  3. Estimates of the proportion, p • When nphat > 5 and n(1-phat) > 5 • Page 383 • Problem 12.65 page 391 • How many people have common sense? • n=1000 Phat = .07

  4. Interpreting confidence intervals • XX % Confidence intervals e.g. 95% • XX % of all randomly selected samples yield an interval that contains m (or p). Thus, the probability is .xx that this interval contains m (or p). • Tradeoffs • Sample size – Confidence - Precision

  5. Tests of hypotheses about m • When s is known and X is normal or n > 30 • Problem 11.28 page 345; 11.37 page 346 • When s is unknown and X is normal or n > 30 • Problem 12.27 page 373; 12.33 page 374

  6. Tests of hypotheses about p • When nphat> 5 and n(1-phat) > 5 • Problem12.66 page 391

  7. Interpreting tests of hypotheses • Reject H0 • Correct decision or Type I error • Probability of Type I error = p-value < a • Type I error is rejecting a true H0 • Fail torejectH0 • Correct decision or Type II error • Probability of Type II error is unknown • Probability of Type II error and a inversely related • Type II error is failing to reject a false H0

  8. Interpreting p-values • P-value < a • Convincing evidence, sufficient to conclude H1 • a < p-value < .50 • Insufficient evidence to conclude H1 at the stated significance level, a • However, data are consistent with H1 • .50 < p-value • No evidence for H1 • Data are consistent with H0

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