Question

a) If random samples of size 12 are drawn from a population with mean 7 and standard deviation 2 , find the standard error of the distribution of sample means.

b) Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean. Find endpoints of a t-distribution with 0.025 beyond them in each tail if the sample has size n=26.

c) Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean. Find endpoints of a t-distribution with 0.005 beyond them in each tail if the sample has size n=30.

Answer 1

( a )

standard error of the distribution of sample means =

                                                                          = 2 / sqrt ( 12 )

                                                                          = 0.577350269

                                                                          = 0.5774

( b )

df = 26 -1 = 25

InvT( 0.025 , 25 ) = 2.110

Answer : 2.110

( c )

df = 30 -1 = 29

InvT( 0.005 , 29 ) = 2.756

Answer : 2.756