# day15 - Population Mean Unknown When we know the value of...

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Population Mean: σ Unknown When we know the value of σ , an interval estimate with conﬁdence coeﬃcient (1 - α ) is ¯ x ± z α/ 2 σ n We derived this interval using the fact that the sampling distribution of ¯ x was normal. We can replace σ with s , the sample standard deviation. When we dont know the value of σ , we can no longer use the normal distribution. Instead we use the t distribution. 1

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The t Distribution There is a separate t distribution for each sample size, n . The t distribution depends on a parameter called the degrees of freedom. The degrees of freedom is equal to n - 1. Each t distribution is symmetric around zero and bell shaped. As the degrees of freedom increase, the t distribution looks more like a standard normal distribution. 2
Table 2 in Appendix B (p. 920-922) contains probabilities for the t distribution. We let t α/ 2 be the number such that an area of α/ 2 is in the upper tail of the t distribution: For 5 degrees of freedom,

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## This note was uploaded on 01/24/2011 for the course STATISTICS 19897 taught by Professor Jager,abigaill during the Fall '10 term at Kansas State University.

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day15 - Population Mean Unknown When we know the value of...

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