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Unformatted text preview: STAT 2053 – Elementary Statistics Chapter 17 – Inference about a Population Mean 1 Chapter 17 This chapter revisits confidence intervals and tests of significance for . This time though, we no longer μ assume that we know the population standard deviation, . σ The first two assumptions from Chapter 14 still apply, however. 2 Chapter 17 3 Conditions for Inference about a Mean • Data are from a SRS of size n . • Population has a Normal distribution with mean m and standard deviation s . • Both m and s are usually unknown. – we use inference to estimate m . – Problem: s unknown means we cannot use the z procedures previously learned. • The population must be much larger than our sample (at least 20 times as large). This assumption is much more practical than assuming we know . σ BPS  5th Ed. Chapter 17 4 • When we do not know the population standard deviation σ (which is usually the case), we must estimate it with the sample standard deviation s . • When the standard deviation of a statistic is estimated from data, the result is called the standard error of the statistic. • The standard error of the sample mean is Standard Error x s n Chapter 17 5 • When we estimate s with s , our onesample z statistic becomes a onesample t statistic . • By changing the denominator to be the standard error, our statistic no longer follows a Normal distribution. The t test statistic follows a t distribution with n – 1 degrees of freedom . • The shorthand for this distribution is: t(n1) • The degrees of freedom (df) specify which t distribution we are using....
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This note was uploaded on 09/23/2011 for the course STAT 2053 taught by Professor Staff during the Fall '08 term at Oklahoma State.
 Fall '08
 staff
 Statistics

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