Lecture15_ch7

# Lecture15_ch7 - Lecture 15 Stat 350 7.5 Small Sample...

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Lecture 15 Stat 350 7.5 Small Sample Confidence Intervals for Two Population Means

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Agenda Topic 1: 7.4 small-sample CI Assumptions and Formula Example Topic 2: (7.5) Two Sample t interval Comparing the difference of two population means for small sample size Two Independent Samples Paired Data
7.4 Small-sample CIs Sample size n: small Assumption on Population Distribution: Approximately Normal When sample size is large (n≥40) Any assumptions on the population distribution? Why?

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T Distribution (df=n-1) The standardized value has a distribution called the t (or Student’s t ) distribution: with n 1 degrees of freedom (df). n s X t
t distribution

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t distribution The higher the degrees of freedom (df) are, the narrower the spread of the t distribution It is more spread than the normal, especially if the df are small As the df increase, the t density curve approaches the N (0, 1) curve more closely When df ∞, t z (standard normal) 0 df = n 2 df = n 1 n 1 < n 2
One sample t confidence interval One sample t confidence interval t critical value from a t distribution with df = n 1 n s value) critical ( t X

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Lecture15_ch7 - Lecture 15 Stat 350 7.5 Small Sample...

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