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Interval Estimation Part II

Interval Estimation Part II. Notes of STAT6205 by Dr. Fan. Overview. Sections 6.4 to 6.6 Introduction Confidence Intervals for variances One variance Ratio of two variances Confidence Intervals for proportions One proportion Difference of two proportions Sample size.

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Interval Estimation Part II

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  1. Interval EstimationPart II Notes of STAT6205 by Dr. Fan 6205-ch6

  2. Overview • Sections 6.4 to 6.6 • Introduction • Confidence Intervals for variances • One variance • Ratio of two variances • Confidence Intervals for proportions • One proportion • Difference of two proportions • Sample size 6205-ch6

  3. Confidence Intervals for One Variance s^2 • Condition: normal population Find the two optimal divisors (a, b) from Table X 6205-ch6

  4. Example Suppose the heights of female students on campus has a normal distribution. In a random sample of 21 students, we find that sample mean is 66 inches and sample S.D. is 3 inches. Find a 95% C.I. for variance. 6205-ch6

  5. F Distribution Definition: Q: What is the distribution of X^-1 where X ~ F(n,m)? 6205-ch6

  6. Confidence Intervals for 6205-ch6

  7. 6205-ch6

  8. 6205-ch6

  9. 6205-ch6

  10. Proportions “p-hat” Chapter 19 The proportion of a population that has some outcome (“success”) is p. The proportion of successes in a sample is measured by the sample proportion:

  11. Inference about a ProportionSimple Conditions Chapter 19

  12. Inference about a ProportionSampling Distribution Chapter 19

  13. Building a Confidence IntervalPopulation Proportion Chapter 19

  14. Standard Error Chapter 19 Since the population proportion p is unknown, the standard deviation of the sample proportion will need to be estimated by substituting for p.

  15. Confidence Interval 10 Chapter 19

  16. Confidence Interval for One Proportion • Example: Suppose we want to estimate p, the proportion of people who favor Proposition A. When a SRS of size 81 is taken, 23 respond in favor of Prop A. Calculate a 90% CI for p. 6205-ch6

  17. Confidence Interval for Difference of Two Proportions • Condition: Two “large” independent samples • Therefore, the (1-a) CI for p1-p2 is 6205-ch6

  18. Is the prevalence of a disease higher in LA or SF? Suppose we too SRSs of size 1500 and 1400 from LA and SF respectively to answer this question. We find that in LA, 115 individuals have the disease and in SF, 189 individuals have the disease. Find a 95% CI for PLA –PSF. What can you conclude? 6205-ch6

  19. Sample Size • How big of a sample size will we need to ensure the precision of our interval? • Required sample size for estimating a mean • Required sample size for estimating a proportion 6205-ch6

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