Chapter 17 - STAT 2053 Elementary Statistics Chapter 17...

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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 assume that we know the population standard deviation, . 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 . BPS - 5th Ed. Chapter 17 4 When we do not know the population standard deviation (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 one-sample z statistic becomes a one-sample 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(n-1) The degrees of freedom (df) specify which t distribution we are using....
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Chapter 17 - STAT 2053 Elementary Statistics Chapter 17...

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