UASTAT141Ch23

UASTAT141Ch23 - Ch 23 CI for a Population Mean common...

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Unformatted text preview: Ch. 23 - CI for a Population Mean- common situation is that σ is unknown, so the sample data must estimate it. Recall n Y Z / σ µ − = . We now have t n s Y Z = − ≠ / µ , where t is a diff. standardized variable. The value of s may not be all that close to σ , especially when n is small. Consequently, there is extra variability and the distribution of t is more spread out than the z curve. t-distributions : As with normal curves, there exists a family of t-curves. The normal distribution has 2 parameters: μ and σ ; the t-distribution has a single parameter: degrees of freedom ( df ). Range of t : similar to range of z ; range of df : 1, 2, 3, …, ∞ Properties of the t-distribution : 1. The t-curve, with any fixed df , is bell-shaped and centered at 0 (just like z-curve). 2. Each t-curve is more spread out than the z-curve. t α /2 > z α /2 3. As df increases, the spread of corresponding t-curve decreases. 4. As df increases, the corresponding sequence of t-curves approaches the z-curve. Let y 1 , y 2 , …, y n constitute a random sample from a normal population distribution. Then the probability distribution of the standardized variable n s Y t / µ − = ~...
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UASTAT141Ch23 - Ch 23 CI for a Population Mean common...

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