Chapter 3 Confidence Interval Revby Rao

Medical Statistics (full English class) ,[object Object],[object Object],[object Object],Slides adapted from Professor Fang Ji-Qian’s

[object Object],[object Object],[object Object]

For several samples from the same population ,[object Object],[object Object],[object Object],[object Object]

3.1 The Distribution of Sample Mean ,[object Object],[object Object],[object Object],[object Object],[object Object]

Features of sample mean as a random variable ,[object Object],[object Object]

(3) The distribution of sample means follows certain rule that more in center, less in two ends and symmetry around the center. (4) The range of variation for the sample mean is much narrower than that of the initial variable.

If the random samples with n individuals are drawn from a normal distribution , then the sample mean follows a normal distribution (3.1) , then the sample mean follows a normal distribution (3.1)

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

3.1.2 Distribution of sample mean from a population with non-normal distribution ,[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object]

3.2 t Distribution ,[object Object],[object Object],W.S. Gosett (1908) explored its distribution

3.2.2 The probability density and critical values of t distribution

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

3.3 The Confidence Interval for Population Mean of Normal Distribution Therefore, 95% of the sample means meet the inequality (but not all) For any sample, if we claim is located in such an interval, then in theory, we might be right about 95 times out of 100 times. and are unknown A sample is drawn, and ,

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

3.4 Confidence Interval for the Difference between Two Population Means unknown. Two samples with The confidence interval for ?

3.5 Confidence Intervals for Probability and the Difference between Two Probabilities ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Comparing to the confidence interval of

3.5.2 Confidence intervals for two population probabilities

3.6 The Sample Size for Estimation of Confidence Interval ,[object Object],3.6.1 Sample size for confidence interval of the mean of normal population Given (1) the confidence level (1-  ) (2) the half width of confidence interval δ (3) the estimate of the standard deviation s Let Replace with , approximately

3.6.2 Sample size for confidence interval of the probability of binomial population ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Summary ,[object Object],[object Object],[object Object]

Chapter 3 Confidence Interval Revby Rao

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Chapter 3 Confidence Interval Revby Rao