STAT 400 Lecture AL1 Spring 2015 Dalpiaz Examples for 5 5 7 1 X 1 X 2 X n be i i d N 2 Let Let X S 2 X i n X 1 X 2 X n sample mean n X i X 2 sample variance n 1 Then X and S 2 are independent 2 X has N n X distribution has N 0 1 distribution n X i 2 2 2 n has n 1 S 2 X i X 2 X has S distribution 2 2 has 2 n 1 distribution t n 1 distribution n A 1 100 confidence interval for the population mean x z 2 n x t 2 s n n 1 degrees of freedom William Gosset 1876 1937 The t Distribution EXCEL TINV v TDIST t v 1 t for t distribution with v degrees of freedom gives 2 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 a 12 18 13 21 15 8 Compute the sample mean and the sample standard deviation 17 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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