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h5 - Confidence Interval Formulas

h5 - Confidence Interval Formulas - STAT 201 Handout 5...

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STAT 201 — Handout 5 Confidence Interval Formulas Setup Identify population(s) and sample(s). Identify unknown parameter to be estimated. Is population SD known? Identify observed sample statistics used in parameter estimation. e.g. Want to know μ = mean GPA of all S201 students . Obtain random sample of n S201 students and use sample mean GPA ( x ) to estimate population mean GPA. This estimate has a typical error of size SD ( X ) = σ/ n . If σ is known, use it. If not, approximate it by s (sample SD). The book calls the approximated SD ( X ) the standard error or SE ( X ). Use of s may or may not require t -distribution in C.I. formula (see below). e.g. Similar to above, but want to know p = proportion of all S201 students who wish to graduate with a Statistics major’s degree . Use b p to estimate p . This estimate has a typical error of size SD ( b p ) = p p (1 - p ) /n , but as p is in the process of being estimated, we must use b p in place of p in the SD formula. The book calls this estimated SD ( b p ) the standard error or SE ( b p ).
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