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UIUC STAT 400 - 400Ex7_1_2

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STAT 400 Lecture AL1 Examples for 5.5, 7.1 Spring 2015 Dalpiaz Let X 1 , X 2 , … , X n be i.i.d.  2σμ , N . Let nnn...i XXXXX21 ( sample mean ) 1XXS22n i ( sample variance ) Then X and S 2 are independent; X has  2σμ , nN distribution; n σμX  has  10 , N distribution; 22σμX i has  2 ( n ) distribution; 2222σσXXS1 i n has  2 ( n – 1 ) distribution; n SXμ has t ( n – 1 ) distribution. A (1  ) 100% confidence interval for the population mean  nzx σ2α  nstx 2α  n – 1 degrees of freedomWilliam Gosset(1876-1937) The t Distribution EXCEL: = TINV (  , v ) gives 2αt for t distribution with v degrees of freedom = TDIST ( t , v , 1 ) gives the upper tail probability for t distribution with v degrees of freedom, P ( T > t ). = TDIST ( t , v , 2 ) gives 2  P ( T > t ).1. A manufacturer of TV sets wants to find the average selling price of a particular model. A random sample of 25 different stores gives the mean selling price as $342 with a sample standard deviation of $14. Assume the prices are normally distributed. Construct a 95% confidence interval for the mean selling price of the TV model. 2. The following random sample was obtained from N (  ,  2 ) distribution: 16 12 18 13 21 15 8 17 a) Compute the sample mean and the sample standard deviation.2. (continued) b) Construct a 95% confidence interval for . c) Construct a 90% confidence upper bound for . d) Construct a 99% confidence lower bound for


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UIUC STAT 400 - 400Ex7_1_2

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